Professor Shahn MajidProfessor of MathematicsEmail: s.majid@qmul.ac.ukTelephone: +44 (0)20 7882 5450Room Number: Mathematical Sciences Building, Room: MB-512Website: https://webspace.maths.qmul.ac.uk/s.majid/Welcome.htmlOffice Hours: Please email me for an appointment in person or on Zoom during term timeProfilePublicationsProfileShahn Majid works particularly on algebraic methods for quantum gravity and other areas where quantum theory and geometry collide, including Hopf algebras (quantum groups) and noncommutative geometry. He pioneered the modern approach to the quantum spacetime hypothesis, the idea that the coordinates x,y,z,t that determine where and when an event takes place are in fact elements of a quantum algebra and hence subject to quantum uncertainty, due to quantum gravity effects. This allows one to understand the nature of physics at the mysterious Planck scale as a practical alternative to so-called Theories of Everything such as string theory. His approach entails the generalisation of the basic concepts of differential calculus and geometry to a suitable quantum Riemannian geometry as well as quantum groups as generalisation of the concept of symmetry that he earlier helped pioneer in the 1980s. His work includes both quantum black holes and baby quantum gravity models where the Universe is modelled by a small graph. He is also responsible for a theory of braided algebra in the early 1990s where algebraic expressions are wired up like in a computer. Such string diagrams have proven popular in computer science and he is also currently interested in applying all of these ideas to quantum information and quantum computing. Shahn Majid is the author of 4 books. His 600 page text Foundations of Quantum Group Theory remains a bible for researchers in the field. His Quantum Groups Primer covers a lecture course from when he was in Cambridge. On Space and Time is a book of collected essays including his own and those of luminaries such as Roger Penrose and the Alain Connes. His new 2020 book, with Beggs, is an 800 page monograph Quantum Riemannian Geometry laying out the new formalism. For more details on all of the above, see his personal website https://webspace.maths.qmul.ac.uk/s.majid/Welcome.html Shahn Majid was educated with 1st degree from Cambridge, including part III of the maths tripos, and with a PhD from Harvard. After a year in Swansea, he spent ten years in Cambridge and as a Fellow of Pembroke College there, moving to Queen Mary in 1999. He was Director of Pure Mathematics 2010-13 and has been an EPSRC Postdoctoral Fellow, an EPSRC Advanced Fellow, a Royal Society University Research Fellow and a Leverhulme Senior Research Fellow. As well as regular research and teaching, Shahn Majid is joint director of the London Taught Course Centre, which provides graduate-level courses for a consortium of universities in London and beyond. See www.ltcc.ac.uk ResearchPublications Majid S (2025). Hopf algebras and q -deformation quantum groups: an overview journal nameOfConference. 10.1016/b978-0-323-95703-8.00221-4 qmroHref Beggs E, Majid S (publicationYear). Quantum geodesic flows on graphs Letters in Mathematical Physics nameOfConference. 10.1007/s11005-024-01860-6 qmroHref Liu C, Majid S (publicationYear). Yang-Mills field from fuzzy sphere quantum Kaluza-Klein model Journal of High Energy Physics nameOfConference. 10.1007/jhep07(2024)195 https://qmro.qmul.ac.uk/xmlui/handle/123456789/99242 Lira-Torres E, Majid S (publicationYear). Geometric Dirac operator on noncommutative torus and M2(C) Letters in Mathematical Physics nameOfConference. 10.1007/s11005-024-01806-y https://qmro.qmul.ac.uk/xmlui/handle/123456789/96118 Majid S (2024). Dirac operator associated to a quantum metric Journal of Noncommutative Geometry nameOfConference. 10.4171/jncg/570 https://qmro.qmul.ac.uk/xmlui/handle/123456789/99240 Beggs E, Majid S (2024). Quantum geodesics in quantum mechanics Journal of Mathematical Physics nameOfConference. 10.1063/5.0154781 https://qmro.qmul.ac.uk/xmlui/handle/123456789/96202 Beggs E, Majid S (2023). Quantum geodesic flow on the integer lattice line Journal of Physics Conference Series nameOfConference. 10.1088/1742-6596/2667/1/012016 https://qmro.qmul.ac.uk/xmlui/handle/123456789/96203 Han X, Majid S (2023). Hopf-Galois extensions and twisted Hopf algebroids Journal of Algebra nameOfConference. 10.1016/j.jalgebra.2023.11.025 https://qmro.qmul.ac.uk/xmlui/handle/123456789/92345 Cowtan A, Majid S (2023). Algebraic aspects of boundaries in the Kitaev quantum double model Journal of Mathematical Physics nameOfConference. 10.1063/5.0127285 https://qmro.qmul.ac.uk/xmlui/handle/123456789/92622 Liu C, Majid S (2023). Quantum Kaluza-Klein theory with M 2(ℂ) Journal of High Energy Physics nameOfConference. 10.1007/JHEP09(2023)102 https://qmro.qmul.ac.uk/xmlui/handle/123456789/91219 Majid S (publicationYear). Algebras and Hopf Algebras in Braided Categories journal nameOfConference. 10.1201/9781003419792-4 https://qmro.qmul.ac.uk/xmlui/handle/123456789/96447 Beggs E, Majid S (2023). Quantum geodesic flows and curvature Letters in Mathematical Physics nameOfConference. 10.1007/s11005-023-01687-7 https://qmro.qmul.ac.uk/xmlui/handle/123456789/92342 Argota-Quiroz JN, Majid S (2023). Quantum Riemannian geometry of the discrete interval and q-deformation Journal of Mathematical Physics nameOfConference. 10.1063/5.0133982 https://qmro.qmul.ac.uk/xmlui/handle/123456789/89319 Majid S (2023). Quantum geometry of Boolean algebras and de Morgan duality Journal of Noncommutative Geometry nameOfConference. 10.4171/jncg/460 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/69426 Argota-Quiroz JN, Majid S (2022). Quantum gravity on finite spacetimes and dynamical mass Proceedings of Science Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity". 10.22323/1.406.0210 https://qmro.qmul.ac.uk/xmlui/handle/123456789/83781 Liu C, Majid S (2022). Quantum geodesics on quantum Minkowski spacetime Journal of Physics A: Mathematical and General nameOfConference. 10.1088/1751-8121/ac7593 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/84502 Majid S (2022). Quantum and braided ZX calculus Journal of Physics A: Mathematical and Theoretical nameOfConference. 10.1088/1751-8121/ac631f https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/78396 Argota-Quiroz JN, Majid S (2022). Quantum Riemannian geometry of the discrete interval and q-deformation Journal of Mathematical Physics nameOfConference. 10.1063/5.0133982 https://qmro.qmul.ac.uk/xmlui/handle/123456789/84500 Cowtan A, Majid S (2022). Quantum double aspects of surface code models Journal of Mathematical Physics nameOfConference. 10.1063/5.0063768 https://qmro.qmul.ac.uk/xmlui/handle/123456789/78397 Majid S, Lira Torres E (2022). Geometric Dirac operator on the fuzzy sphere Letters in Mathematical Physics nameOfConference. 10.1007/s11005-021-01499-7 https://qmro.qmul.ac.uk/xmlui/handle/123456789/76206 Argota-Quiroz JN, Majid S (2021). Fuzzy and discrete black hole models* *The first author was partially supported by CONACyT (México). Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/abfea6 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/72186 Majid S, Lira Torres E (2021). Quantum gravity and Riemannian geometry on the fuzzy sphere Letters in Mathematical Physics nameOfConference. 10.1007/s11005-021-01359-4 https://qmro.qmul.ac.uk/xmlui/handle/123456789/70303 Majid S, Williams L (2021). Poisson principal bundles Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) nameOfConference. 10.3842/SIGMA.2021.006 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/70117 Majid S, Argota Quiroz J (2020). Quantum gravity on polygons and R x Z_n FLRW mode Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/abbaa8 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/67444 Majid S, Pachol A (2020). Digital quantum groups Journal of Mathematical Physics nameOfConference. 10.1063/5.0020958 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/67104 Majid S, AZIZ R (2020). Quantum differentials on cross product Hopf algebras Journal of Algebra nameOfConference. 10.1016/j.jalgebra.2020.06.024 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/65963 Majid S, Pacho A (2020). Digital finite quantum Riemannian geometries Journal of Physics A: Mathematical and Theoretical nameOfConference. 10.1088/1751-8121/ab1cf2 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/57786 Majid S (2020). Reconstruction and quantization of Riemannian structures Journal of Mathematical Physics nameOfConference. 10.1063/1.5123258 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/62505 Beggs EJ, Majid S (2020). Quantum Riemannian Geometry journal nameOfConference. 10.1007/978-3-030-30294-8 qmroHref Majid S (2020). Quantum geometry, logic and probability Zagadnienia Filozoficzne w Nauce nameOfConference. doi qmroHref Majid S (2019). Quantum gravity on a square graph Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/ab4975 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/60117 Majid S, Tao W-Q (2019). Generalised noncommutative geometry on finite groups and Hopf quivers Journal of Noncommutative Geometry nameOfConference. 10.4171/jncg/345 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/36407 Majid S (2019). Quantum Riemannian geometry and particle creation on the integer line Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/ab2424 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/57788 Albuquerque H, Majid S (2019). New approach to octonions and Cayley algebras journal nameOfConference. 10.1201/9780429187674-1 qmroHref Bassett ME, Majid S (2020). Finite Noncommutative Geometries Related to Fp[x] Algebras and Representation Theory nameOfConference. 10.1007/s10468-018-09846-4 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/54656 Aziz R, Majid S (2019). Co-double bosonisation and dual bases of c q [SL 2] and c q [SL 3] Journal of Algebra nameOfConference. 10.1016/j.jalgebra.2018.09.034 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/45744 Akylzhanov R, Majid S, Ruzhansky M (2018). Smooth Dense Subalgebras and Fourier Multipliers on Compact Quantum Groups Communications in Mathematical Physics nameOfConference. 10.1007/s00220-018-3219-4 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/39786 MAJID SH (2018). On the Emergence of the Structure of Physics Philosophical Transactions A: Mathematical, Physical and Engineering Sciences nameOfConference. 10.1098/rsta.2017.0231 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/36207 MAJID SH, PACHOL A (2018). Classification of digital affine noncommutative geometries Journal of Mathematical Physics nameOfConference. 10.1063/1.5025815 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/36296 MAJID SH, WILLIAMS L (2018). Quantum Koszul formula on quantum spacetime Journal of Geometry and Physics nameOfConference. 10.1016/j.geomphys.2018.02.012 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/36209 MAJID SH, Osei P (2018). Quasitriangular structure and twisting of the 3D bicrossproduct model Journal of High Energy Physics nameOfConference. 10.1007/JHEP01(2018)147 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/32330 MAJID SH, Beggs EJ (2017). Quantum Bianchi identities via DG categories Journal of Geometry and Physics nameOfConference. 10.1016/j.geomphys.2017.11.005 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/28960 MAJID SH, Beggs EJ (2017). Spectral triples from bimodule connections and Chern connections Journal of Noncommutative Geometry nameOfConference. 10.4171/JNCG/11-2-7 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/15041 Fritz C, Majid S (2017). Noncommutative spherically symmetric spacetimes at semiclassical order Classical and Quantum Gravity nameOfConference. 10.1088/1361-6382/aa72a5 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/24660 MAJID SH (2017). Quantum Riemannian geometry of phase space and nonassociativity Demonstratio Mathematica nameOfConference. 10.1515/dema-2017-0009 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/17793 MAJID SH (2017). Hodge Star as Braided Fourier Transform Algebras and Representation Theory nameOfConference. 10.1007/s10468-016-9661-0 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/17781 MAJID SH, Lopez Pena J, Rietsch K (2017). Lie theory of finite simple groups and Roth property Cambridge Philosophical Society: Mathematical Proceedings nameOfConference. 10.1017/S030500411600102X https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/18001 MAJID SH, Beggs EJ (2016). Poisson-Riemannian geometry Journal of Geometry and Physics nameOfConference. 10.1016/j.geomphys.2016.12.012 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/18458 Majid S (2017). Non-commutative Differential Geometry journal nameOfConference. 10.1142/9781786341006_0005 qmroHref Majid S (2002). Knots and Feynman diagrams, by D. Kreimer. Pp. 272. £21.95. 2000. ISBN 0521 58761 1 (Cambridge University Press). The Mathematical Gazette nameOfConference. 10.2307/3621922 qmroHref Majid S, Tao W-Q (publicationYear). Noncommutative differentials on Poisson–Lie groups and pre-Lie algebras Pacific Journal of Mathematics nameOfConference. 10.2140/pjm.2016.284.213 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/12484 Majid S, Tao W-Q (2015). Duality for generalised differentials on quantum groups Journal of Algebra nameOfConference. 10.1016/j.jalgebra.2015.03.023 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/31972 Majid S, Tao W-Q (2015). Cosmological constant from quantum spacetime Physical Review D nameOfConference. 10.1103/physrevd.91.124028 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/7960 MAJID SH (2014). The self-representing Universe journal nameOfConference. doi https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/12064 Polkinghorne J, Penrose R, Taylor A et al. (2012). Quantum spacetime and physical reality journal nameOfConference. 10.1017/cbo9781139197069.003 qmroHref Majid S (2014). Emergence of Riemannian geometry and the massive graviton 2ND INTERNATIONAL CONFERENCE ON NEW FRONTIERS IN PHYSICS nameOfConference. 10.1051/epjconf/20147100080 qmroHref Beggs EJ, Majid S (2014). Gravity induced from quantum spacetime CLASSICAL AND QUANTUM GRAVITY nameOfConference. 10.1088/0264-9381/31/3/035020 https://uat2-qmro.qmul.ac.uk/xmlui/handle/123456789/8149 Majid S (2014). Newtonian gravity on quantum spacetime 1ST INTERNATIONAL CONFERENCE ON NEW FRONTIERS IN PHYSICS nameOfConference. 10.1051/epjconf/20147000082 qmroHref Connes A, Heller M, Penrose R et al. (2008). Quantum spacetime and physical reality journal nameOfConference. 10.1017/cbo9781139644259.003 qmroHref Majid S, Rietsch K (2013). Lie theory and coverings of finite groups JOURNAL OF ALGEBRA nameOfConference. 10.1016/j.jalgebra.2013.02.042 qmroHref Majid S (2013). Noncommutative Riemannian geometry on graphs JOURNAL OF GEOMETRY AND PHYSICS nameOfConference. 10.1016/j.geomphys.2013.02.004 qmroHref Majid S (1993). BRAIDED GROUPS AND BRAID STATISTICS journal nameOfConference. 10.1142/9789812812810_0021 qmroHref Majid S (1991). QUANTUM GROUPS AND QUANTUM PROBABILITY journal nameOfConference. 10.1142/9789814360203_0021 qmroHref MAJID S, SOIBELMAN YS (1991). CHERN-SIMONS THEORY, MODULAR FUNCTIONS AND QUANTUM MECHANICS IN AN ALCOVE International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x91000940 qmroHref MAJID S (1990). ON q-REGULARIZATION International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x90001999 qmroHref MAJID S (1993). QUANTUM RANDOM WALKS AND TIME REVERSAL International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x93001818 qmroHref MAJID S (1990). QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x90000027 qmroHref MAJID S (1991). RECONSTRUCTION THEOREMS AND RATIONAL CONFORMAL FIELD THEORIES International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x91002100 qmroHref MACFARLANE AJ, MAJID S (1992). SPECTRUM GENERATING QUANTUM GROUP OF THE HARMONIC OSCILLATOR International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x92001952 qmroHref MAJID S (2000). CONCEPTUAL ISSUES FOR NONCOMMUTATIVE GRAVITY ON ALGEBRAS AND FINITE SETS International Journal of Modern Physics B nameOfConference. 10.1142/s0217979200001953 qmroHref AMELINO-CAMELIA G, MAJID S (2000). WAVES ON NONCOMMUTATIVE SPACE–TIME AND GAMMA-RAY BURSTS International Journal of Modern Physics A nameOfConference. 10.1142/s0217751x00002779 qmroHref Majid S (2012). Almost Commutative Riemannian Geometry: Wave Operators COMMUNICATIONS IN MATHEMATICAL PHYSICS nameOfConference. 10.1007/s00220-012-1416-0 qmroHref Majid S (2012). Emergence of Wave Equations from Quantum Geometry SIXTH INTERNATIONAL SCHOOL ON FIELD THEORY AND GRAVITATION-2012 nameOfConference. 10.1063/1.4756969 qmroHref Connes A, Heller M, Majid S et al. (2012). On space and time journal nameOfConference. 10.1017/CBO9781139197069 qmroHref Majid S (2012). Preface On Space and Time nameOfConference. 10.1017/CBO9781139197069.001 qmroHref MAJID S (1999). DIAGRAMMATICS OF BRAIDED GROUP GAUGE THEORY Journal of Knot Theory and Its Ramifications nameOfConference. 10.1142/s021821659900047x qmroHref MAJID S (1995). SOLUTIONS OF THE YANG-BAXTER EQUATIONS FROM BRAIDED-LIE ALGEBRAS AND BRAIDED GROUPS Journal of Knot Theory and Its Ramifications nameOfConference. 10.1142/s0218216595000284 qmroHref Gateva-Ivanova T, Majid S (2011). Quantum Spaces Associated to Multipermutation Solutions of Level Two ALGEBR REPRESENT TH nameOfConference. 10.1007/s10468-009-9192-z qmroHref Beggs EJ, Majid S (2011). *-compatible connections in noncommutative Riemannian geometry J GEOM PHYS nameOfConference. 10.1016/j.geomphys.2010.09.002 qmroHref Majid S (2011). q-Fuzzy Spheres and Quantum Differentials on Bq[SU2] and Uq(su2) LETTERS IN MATHEMATICAL PHYSICS nameOfConference. 10.1007/s11005-011-0523-8 qmroHref TOMASIC I, Majid S (2011). On braided zeta functions Bull. Math. Sci. nameOfConference. 10.1007/s13373-011-0006-3 qmroHref Majid S (2011). Scaling Limit of the Noncommutative Black Hole GROUP 28: PHYSICAL AND MATHEMATICAL ASPECTS OF SYMMETRY: PROCEEDINGS OF THE 28TH INTERNATIONAL COLLOQUIUM ON GROUP-THEORETICAL METHODS IN PHYSICS nameOfConference. 10.1088/1742-6596/284/1/012003 qmroHref Beggs E, Majid S (2010). Nonassociative Riemannian geometry by twisting Journal of Physics Conference Series nameOfConference. 10.1088/1742-6596/254/1/012002 qmroHref Majid S (2010). Quantum groups journal nameOfConference. doi qmroHref Klim J, Majid S (2010). Hopf quasigroups and the algebraic 7-sphere J ALGEBRA nameOfConference. 10.1016/j.jalgebra.2010.03.011 qmroHref Beggs EJ, Majid S (2010). Quantization by cochain twists and nonassociative differentials J MATH PHYS nameOfConference. 10.1063/1.3371677 qmroHref Klim J, Majid S (2010). Bicrossproduct Hopf quasigroups Commentationes Mathematicae Universitatis Carolinae nameOfConference. doi qmroHref Majid S, Connes A, Heller M et al. (2010). On space and time journal nameOfConference. 10.1017/CBO9781139644259 qmroHref Majid S (2010). Preface On Space and Time nameOfConference. 10.1017/CBO9781139644259.001 qmroHref Majid S (2009). Algebraic approach to Quantum Gravity II: noncommutative spacetime journal nameOfConference. 10.1017/cbo9780511575549.029 qmroHref Majid S, Schroers BJ (2009). q-deformation and semidualization in 3D quantum gravity J PHYS A-MATH THEOR nameOfConference. 10.1088/1751-8113/42/42/425402 qmroHref Beggs EJ, Majid S (2009). Bar Categories and Star Operations ALGEBRAS AND REPRESENTATION THEORY nameOfConference. 10.1007/s10468-009-9141-x qmroHref Brain SJ, Majid S (2008). Quantisation of Twistor Theory by Cocycle Twist COMMUN MATH PHYS nameOfConference. 10.1007/s00220-008-0607-1 qmroHref Majid S, Markl M (1996). Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type Mathematical Proceedings of the Cambridge Philosophical Society nameOfConference. 10.1017/s0305004100074041 qmroHref Majid S (1993). Transmutation theory and rank for quantum braided groups Mathematical Proceedings of the Cambridge Philosophical Society nameOfConference. 10.1017/s0305004100075769 qmroHref Freidel L, Majid S (2008). Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity CLASSICAL QUANT GRAV nameOfConference. 10.1088/0264-9381/25/4/045006 qmroHref Gateva-Ivanova T, Majid S (2008). Matched pairs approach to set theoretic solutions of the Yang-Baxter equation J ALGEBRA nameOfConference. 10.1016/j.jalgebra.2007.10.035 qmroHref Majid S (1991). Gauge-covariant vacuum expectations and glueballs Il Nuovo Cimento A (1971-1996) nameOfConference. 10.1007/bf02813352 qmroHref Majid S (1991). Mass dependence ofU(1) axial-symmetry breakdown Il Nuovo Cimento A (1971-1996) nameOfConference. 10.1007/bf02821772 qmroHref Majid S (1989). Canonical arbitrary-spin background-field wave operator and applications Il Nuovo Cimento A (1971-1996) nameOfConference. 10.1007/bf02800156 qmroHref Gateva-Ivanova T, Majid S (2007). Set-theoretic solutions of the Yang-Baxter equation, graphs and computations JOURNAL OF SYMBOLIC COMPUTATION nameOfConference. 10.1016/j.jsc.2007.06.007 qmroHref Hadfield T, Majid S (2007). Bicrossproduct approach to the Connes-Moscovici Hopf algebra J ALGEBRA nameOfConference. 10.1016/j.jalgebra.2006.09.031 qmroHref Majid S (2007). Algebraic approach to quantum gravity III: Non-commmutative riemannian geometry Quantum Gravity: Mathematical Models and Experimental Bounds nameOfConference. 10.1007/978-3-7643-7978-0_5 qmroHref Beggs EJ, Majid S (2006). Semiclassical differential structures PAC J MATH nameOfConference. 10.2140/pjm.2006.224.1 qmroHref Majid S (2006). Bicrossproduct Hopf Algebras and Noncommutative Spacetime journal nameOfConference. 10.1016/B0-12-512666-2/00029-8 qmroHref Majid S (2006). Hopf Algebras and q-Deformation Quantum Groups journal nameOfConference. 10.1016/B0-12-512666-2/00028-6 qmroHref MAJID SH (2006). What is a quantum group journal nameOfConference. doi qmroHref Majid S (2005). Gauge theory on nonassociative spaces J MATH PHYS nameOfConference. 10.1063/1.2084747 qmroHref Majid S (2005). Noncommutative model with spontaneous time generation and Planckian bound J MATH PHYS nameOfConference. 10.1063/1.2084748 qmroHref Majid S (2005). Noncommutative Riemannian and spin geometry of the standard q-sphere COMMUN MATH PHYS nameOfConference. 10.1007/s00220-005-1295-8 qmroHref MAJID SH (2005). Classification of differentials on quantum doubles and finite noncommutative geometry journal nameOfConference. 10.1201/9780429187629-10 qmroHref Majid S (2005). Noncommutative differentials and Yang-Mills on permutation groups S-n journal nameOfConference. doi qmroHref Majid S, Raineri E (2004). Moduli of quantum Riemannian geometries on <= 4 points J MATH PHYS nameOfConference. 10.1063/1.1804231 qmroHref Ngakeu F, Majid S, Ezin JP (2004). Cartan calculus for quantum differentials on bicrossproducts ACTA APPL MATH nameOfConference. 10.1007/s10440-004-5592-6 qmroHref Akrami SE, Majid S (2004). Braided cyclic cocycles and nonassociative geometry J MATH PHYS nameOfConference. 10.1063/1.1787621 qmroHref Goldin GA, Majid S (2004). On the Fock space for nonrelativistic anyon fields and braided tensor products J MATH PHYS nameOfConference. 10.1063/1.1787620 qmroHref Majid S (2004). Special issue: Quantum groups and noncommutative geometry - Introduction J MATH PHYS nameOfConference. 10.1063/1.1787622 qmroHref MAJID SH, Akrami SE (2004). Braided cyclic cocycles and nonassociative geometry J. Math. Phys. nameOfConference. 10.1063/1.1787621 qmroHref Majid S (2004). Noncommutative physics on Lie algebras, (Z(2))(n) lattices and Clifford algebras CLIFFORD ALGEBRAS: APPLICATIONS TO MATHEMATICS, PHYSICS, AND ENGINEERING nameOfConference. 10.1007/978-1-4612-2044-2_31 qmroHref Gomez X, Majid S (2003). Braided Lie algebras and bicovdriant differential calculi over co-quasitriangular Hopf algebras J ALGEBRA nameOfConference. 10.1016/S0021-8693(02)00580-X qmroHref Cameron PJ, Majid S (2003). Braided line and counting fixed points of GL(d, F-q) COMMUN ALGEBRA nameOfConference. 10.1081/AGB-120018519 qmroHref Batista E, Majid S (2003). Noncommutative geometry of angular momentum space U(su(2)) J MATH PHYS nameOfConference. 10.1063/1.1517395 qmroHref Batista E, Majid S (2003). Noncommutative geometry on the algebra U(su2) and quantization of coadjoint orbits GROUP 24 : PHYSICAL AND MATHEMATICAL ASPECTS OF SYMMETRIES nameOfConference. doi qmroHref Majid S (2003). Noncommutative ricci curvature and dirac operator on Cq[SL2] at roots of unity LETT MATH PHYS nameOfConference. 10.1023/A:1022980227093 qmroHref MAJID SH, GOMEZ X (2003). Relating quantum and braided Lie algebras journal nameOfConference. doi qmroHref Majid S, Raineri E (2002). Electromagnetism and gauge theory on the permutation group S-3 J GEOM PHYS nameOfConference. 10.1016/S0393-0440(02)00052-9 qmroHref Majid S, Schucker T (2002). Z(2) x Z(2) lattice as a Connes-Lott-quantum group model J GEOM PHYS nameOfConference. 10.1016/S0393-0440(02)00005-0 qmroHref Albuquerque H, Majid S (2002). Clifford algebras obtained by twisting of group algebras J PURE APPL ALGEBRA nameOfConference. 10.1016/S0022-4049(01)00124-4 qmroHref Ngakeu F, Majid S, Lambert D (2002). Noncommutative Riemannian geometry of the alternating group A(4) J GEOM PHYS nameOfConference. 10.1016/S0393-0440(01)00089-4 qmroHref Gomez X, Majid S (2002). Noncommutative cohomology and electromagnetism on C-q[SL2] at roots of unity LETT MATH PHYS nameOfConference. 10.1023/A:1016287607529 qmroHref MAJID SH (2002). A Quantum Groups Primer journal nameOfConference. 10.2277/0521010411 qmroHref Majid S (2002). Riemannian geometry of quantum groups and finite groups with nonuniversal differentials COMMUN MATH PHYS nameOfConference. 10.1007/s002201000564 qmroHref Beggs EJ, Majid S (2001). Poisson-Lie T-duality for quasitriangular Lie bialgebras COMMUN MATH PHYS nameOfConference. 10.1007/s002200100463 qmroHref MAJID SH (2001). Noncommutative differential geometry and twisting of quantum groups journal nameOfConference. doi qmroHref Majid S, Oeckl R (2000). Twisting of Quantum Differentials journal nameOfConference. 10.1007/3-540-46552-9_17 qmroHref Brzeziński T, Majid S (2000). Quantum Geometry of Algebra Factorisations¶and Coalgebra Bundles Communications in Mathematical Physics nameOfConference. 10.1007/pl00005530 qmroHref Majid S (2000). Quantum groups and noncommutative geometry Journal of Mathematical Physics nameOfConference. 10.1063/1.533331 qmroHref Majid S (2000). Non-commutative geometry and quantum groups Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences nameOfConference. 10.1098/rsta.2000.0521 qmroHref Majid S (2000). Braided-Lie bialgebras Pacific Journal of Mathematics nameOfConference. 10.2140/pjm.2000.192.329 qmroHref Majid S (2000). Meaning of noncommutative geometry and the Planck-scale quantum group TOWARDS QUANTUM GRAVITY nameOfConference. doi qmroHref Amelino-Camelia G, Majid S (2000). Waves on noncommutative space-time and gamma-ray bursts INTERNATIONAL JOURNAL OF MODERN PHYSICS A nameOfConference. 10.1142/S0217751X00002777 qmroHref Hajac PM, Majid S (1999). Projective Module Description of the q-Monopole Communications in Mathematical Physics nameOfConference. 10.1007/s002200050704 qmroHref Albuquerque H, Majid S (1999). Quasialgebra Structure of the Octonions Journal of Algebra nameOfConference. 10.1006/jabr.1998.7850 qmroHref Beggs E, Majid S (1999). Quasitriangular and Differential Structures on Bicrossproduct Hopf Algebras Journal of Algebra nameOfConference. 10.1006/jabr.1998.7845 qmroHref Majid S, Oeckl R (1999). Twisting of Quantum Differentials and¶the Planck Scale Hopf Algebra Communications in Mathematical Physics nameOfConference. 10.1007/s002200050692 qmroHref Majid S (1999). Quantum and braided group Riemannian geometry Journal of Geometry and Physics nameOfConference. 10.1016/s0393-0440(98)00051-5 qmroHref Majid S (1999). Quantum geometry of field extensions Journal of Mathematical Physics nameOfConference. 10.1063/1.532866 qmroHref MAJID S (1999). Double-bosonization of braided groups and the construction of Uq(g) Mathematical Proceedings of the Cambridge Philosophical Society nameOfConference. 10.1017/s0305004198002576 qmroHref Majid S (1988). Hopf algebras for physics at the Planck scale Classical and Quantum Gravity nameOfConference. 10.1088/0264-9381/5/12/010 qmroHref Brzeziński T, Majid S (1998). Quantum Differentials and the q-Monopole Revisited Acta Applicandae Mathematicae nameOfConference. 10.1023/a:1006053806824 qmroHref Majid S (1998). Quantum and braided diffeomorphism groups Journal of Geometry and Physics nameOfConference. 10.1016/s0393-0440(98)00016-3 qmroHref Majid S (1998). Some remarks on braided group reconstruction and braided doubles Czechoslovak Journal of Physics nameOfConference. 10.1023/a:1021673726521 qmroHref Majid S (1998). Quantum Double for Quasi-Hopf Algebras Letters in Mathematical Physics nameOfConference. 10.1023/a:1007450123281 qmroHref Majid S (1998). Classification of bicovariant differential calculi Journal of Geometry and Physics nameOfConference. 10.1016/s0393-0440(97)00025-9 qmroHref Brzeziński T, Majid S (1998). Coalgebra Bundles Communications in Mathematical Physics nameOfConference. 10.1007/s002200050274 qmroHref Brzeziński T, Majid S (1998). Line bundles on quantum spheres AIP Conference Proceedings nameOfConference. 10.1063/1.57118 qmroHref Majid S (1997). Fermionic q-Fock space and braided geometry Journal of Mathematical Physics nameOfConference. 10.1063/1.532128 qmroHref Majid S (1997). Quasi-∗ structure on q-Poincaré algebras Journal of Geometry and Physics nameOfConference. 10.1016/s0393-0440(96)00022-8 qmroHref MAJID S (1997). Bicross-Product Structure of Affine Quantum Groups Letters in Mathematical Physics nameOfConference. 10.1023/a:1007318108923 qmroHref Majid S (1997). Some comments on bosonisation and biproducts Czechoslovak Journal of Physics nameOfConference. 10.1023/a:1021013612601 qmroHref Majid S (1997). Anyonic lie algebras Czechoslovak Journal of Physics nameOfConference. 10.1023/a:1022877616496 qmroHref Majid S (1997). Braided geometry and the inductive construction of Lie algebras and quantum groups DEFORMATION THEORY AND SYMPLECTIC GEOMETRY nameOfConference. doi qmroHref Majid S (1997). New quantum groups by double-bosonisation Czechoslovak Journal of Physics nameOfConference. 10.1023/a:1021400329710 qmroHref Majid S (1997). Quantum geometry and the Planck scale GROUP 21 - PHYSICAL APPLICATIONS AND MATHEMATICAL ASPECTS OF GEOMETRY, GROUPS, AND ALGEBRA, VOLS 1 AND 2 nameOfConference. doi qmroHref Majid S (1996). Braided geometry of the conformal algebra Journal of Mathematical Physics nameOfConference. 10.1063/1.531749 qmroHref Beggs EJ, Gould JD, Majid S (1996). Finite Group Factorizations and Braiding Journal of Algebra nameOfConference. 10.1006/jabr.1996.0112 qmroHref Majid S (1996). Introduction to braided geometry and q-Minkowski space QUANTUM GROUPS AND THEIR APPLICATIONS IN PHYSICS nameOfConference. doi qmroHref Majid S, Rodríguez-Plaza MJ (1995). Nonstandard quantum groups and superization Journal of Mathematical Physics nameOfConference. 10.1063/1.531344 qmroHref Majid S (1995). *‐structures on braided spaces Journal of Mathematical Physics nameOfConference. 10.1063/1.530900 qmroHref Majid S (1995). q‐epsilon tensor for quantum and braided spaces Journal of Mathematical Physics nameOfConference. 10.1063/1.531098 qmroHref Brzeziński T, Majid S (1995). Quantum group Gauge theory on quantum spaces Communications in Mathematical Physics nameOfConference. 10.1007/bf02099359 qmroHref Kempf A, Majid S (1994). Algebraic q‐integration and Fourier theory on quantum and braided spaces Journal of Mathematical Physics nameOfConference. 10.1063/1.530644 qmroHref Majid S, Rodríguez-Plaza MJ (1994). Anyonic FRT construction Czechoslovak Journal of Physics nameOfConference. 10.1007/bf01690459 qmroHref Majid S (1994). Some remarks on the quantum double Czechoslovak Journal of Physics nameOfConference. 10.1007/bf01690458 qmroHref Majid S (1994). q‐Euclidean space and quantum Wick rotation by twisting Journal of Mathematical Physics nameOfConference. 10.1063/1.530828 qmroHref Majid S, Ruegg H (1994). Bicrossproduct structure of κ-Poincare group and non-commutative geometry Physics Letters B nameOfConference. 10.1016/0370-2693(94)90699-8 qmroHref Majid S, Rodríguez-Plaza MJ (1994). Random walk and the heat equation on superspace and anyspace Journal of Mathematical Physics nameOfConference. 10.1063/1.530868 qmroHref Lyubashenko V, Majid S (1994). Braided Groups and Quantum Fourier Transform Journal of Algebra nameOfConference. 10.1006/jabr.1994.1165 qmroHref Majid S, Meyer U (1994). Braided matrix structure ofq-Minkowski space andq-Poincaré group Zeitschrift für Physik C Particles and Fields nameOfConference. 10.1007/bf01411029 qmroHref Majid S (1994). On the addition of quantum matrices Journal of Mathematical Physics nameOfConference. 10.1063/1.530527 qmroHref Majid S (1994). Quantum and braided-Lie algebras Journal of Geometry and Physics nameOfConference. 10.1016/0393-0440(94)90014-0 qmroHref Majid S (1994). The quantum double as quantum mechanics Journal of Geometry and Physics nameOfConference. 10.1016/0393-0440(94)90026-4 qmroHref Majid S (1994). Bicrossproduct Structure of the Quantum Weyl Group Journal of Algebra nameOfConference. 10.1006/jabr.1994.1004 qmroHref Gurevich D, Majid S (1994). Braided groups of Hopf algebras obtained by twisting Pacific Journal of Mathematics nameOfConference. 10.2140/pjm.1994.162.27 qmroHref Majid S (1994). Cross Products by Braided Groups and Bosonization Journal of Algebra nameOfConference. 10.1006/jabr.1994.1011 qmroHref Majid S (1994). Lie algebras and braided geometry PROCEEDINGS OF THE XXIITH INTERNATIONAL CONFERENCE ON DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL PHYSICS nameOfConference. doi qmroHref Brzeziński T, Majid S (1993). Quantum group gauge theory on quantum spaces Communications in Mathematical Physics nameOfConference. 10.1007/bf02096884 qmroHref Majid S (1993). Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group Communications in Mathematical Physics nameOfConference. 10.1007/bf02096865 qmroHref Majid S (1993). Free braided differential calculus, braided binomial theorem, and the braided exponential map Journal of Mathematical Physics nameOfConference. 10.1063/1.530326 qmroHref Baskerville WK, Majid S (1993). The braided Heisenberg group Journal of Mathematical Physics nameOfConference. 10.1063/1.530047 qmroHref Majid S, Rodríguez-Plaza MJ (1993). Quantum and super-quantum group related to the Alexander-Conway polynomial Journal of Geometry and Physics nameOfConference. 10.1016/0393-0440(93)90069-q qmroHref Majid S (1993). Braided groups Journal of Pure and Applied Algebra nameOfConference. 10.1016/0022-4049(93)90103-z qmroHref Majid S (1993). Braided momentum in the q‐Poincaré group Journal of Mathematical Physics nameOfConference. 10.1063/1.530154 qmroHref Majid S (1993). Quantum and braided linear algebra Journal of Mathematical Physics nameOfConference. 10.1063/1.530193 qmroHref Majid S (1993). Anyonic Quantum Groups journal nameOfConference. 10.1007/978-94-011-1719-7_38 qmroHref Brzeziński T, Majid S (1993). Quantum group gauge theory on classical spaces Physics Letters B nameOfConference. 10.1016/0370-2693(93)91830-g qmroHref DONIN J, GUREVICH D, MAJID S (1993). R-MATRIX BRACKETS AND THEIR QUANTIZATION ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE nameOfConference. doi qmroHref Majid S (1992). C -statistical quantum groups and Weyl algebras Journal of Mathematical Physics nameOfConference. 10.1063/1.529891 qmroHref Brzeziński T, Majid S (1992). A class of bicovariant differential calculi on hopf algebras Letters in Mathematical Physics nameOfConference. 10.1007/bf00420519 qmroHref Lyubashenko VV, Majid S (1992). Fourier transform identities in quantum mechanics and the quantum line Physics Letters B nameOfConference. 10.1016/0370-2693(92)91926-z qmroHref MAJID S (1992). AN OPEN PROBLEM IN QUANTUM GROUPS LECTURE NOTES IN MATHEMATICS nameOfConference. doi qmroHref MAJID S (1992). RANK OF QUANTUM GROUPS AND BRAIDED GROUPS IN DUAL FORM LECTURE NOTES IN MATHEMATICS nameOfConference. doi qmroHref MACFARLANE AJ, MAJID S (1992). THE SUPERALGEBRA OSP(1/2) AND A RELATED QUANTUM GROUP-STRUCTURE FOR HARMONIC-OSCILLATOR SYSTEMS TOPOLOGICAL AND GEOMETRICAL METHODS IN FIELD THEORY nameOfConference. doi qmroHref Majid S (1991). Examples of braided groups and braided matrices Journal of Mathematical Physics nameOfConference. 10.1063/1.529485 qmroHref Macfarlane AJ, Majid S (1991). Quantum group structure in a fermionic extension of the quantum harmonic oscillator Physics Letters B nameOfConference. 10.1016/0370-2693(91)90924-f qmroHref Majid S (1991). Principle of Representation‐Theoretic Self‐Duality Physics Essays nameOfConference. 10.4006/1.3028923 qmroHref Majid S (1991). Braided groups and algebraic quantum field theories Letters in Mathematical Physics nameOfConference. 10.1007/bf00403542 qmroHref Majid S (1991). Quasi-quantum groups as internal symmetries of topological quantum field theories Letters in Mathematical Physics nameOfConference. 10.1007/bf00405171 qmroHref Majid S, Soibelman YS (1991). Rank of quantized universal enveloping algebras and modular functions Communications in Mathematical Physics nameOfConference. 10.1007/bf02431880 qmroHref Majid S (1991). Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the Classical Yang-Baxter Equations Journal of Functional Analysis nameOfConference. 10.1016/0022-1236(91)90031-y qmroHref Majid S (1991). Doubles of quasitriangular hopf algebras Communications in Algebra nameOfConference. 10.1080/00927879108824306 qmroHref Majid S (1990). Fourier transforms on 𝒜/𝒢 and knot invariants Journal of Mathematical Physics nameOfConference. 10.1063/1.529026 qmroHref Majid S (1990). Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction Journal of Algebra nameOfConference. 10.1016/0021-8693(90)90099-a qmroHref Majid S (1990). More examples of bicrossproduct and double cross product Hopf algebras Israel Journal of Mathematics nameOfConference. 10.1007/bf02764616 qmroHref BEGGS E, MAJID S (1990). MATCHED PAIRS OF TOPOLOGICAL LIE-ALGEBRAS CORRESPONDING TO LIE BIALGEBRA STRUCTURES ON DIFF(S1) AND DIFF(R) ANNALES DE L INSTITUT HENRI POINCARE-PHYSIQUE THEORIQUE nameOfConference. doi qmroHref Majid S (1990). Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations Pacific Journal of Mathematics nameOfConference. 10.2140/pjm.1990.141.311 qmroHref MAJID S (1990). QUANTUM GROUP DUALITY IN VERTEX MODELS AND OTHER RESULTS IN THE THEORY OF QUASI-TRAINGULAR HOPF-ALGEBRAS DIFFERENTIAL GEOMETRIC METHODS IN THEORETICAL PHYSICS nameOfConference. doi qmroHref Majid S (1990). Representation-theoretic rank and double hopf algebras Communications in Algebra nameOfConference. 10.1080/00927879008824103 qmroHref Majid S (1989). Erratum: Liouville theorem for the Yang–Mills self-duality equations [J. Math. Phys. 2 9 , 2303 (1988)] Journal of Mathematical Physics nameOfConference. 10.1063/1.528249 qmroHref Majid S (1989). Partial waves for the linearized Yang–Mills equation about a monopole background Journal of Mathematical Physics nameOfConference. 10.1063/1.528334 qmroHref Majid S (1989). Matched pairs of lie groups and Hopf algebra bicrossproducts Nuclear and Particle Physics Proceedings nameOfConference. 10.1016/0920-5632(89)90488-x qmroHref Majid S (1988). Liouville theorem for the Yang–Mills self-duality equations Journal of Mathematical Physics nameOfConference. 10.1063/1.528204 qmroHref