Publications

 
 

Books and edited volumes


  1. 1.S. Majid, Foundations of Quantum Group Theory Cambridge University Press, (1995) 609 pp. & paperback  (2000)  640 pp

  2. 2.S. Majid, A Quantum Groups Primer, L.M.S. Lect. Notes 292 (2002) 179 pp

  3. 3.S. Majid (Editor), Special Issue: Quantum Groups and Noncommutative Geometry Journal of Mathematical Physics 45 (2004) 311 pp

  4. 4.S. Majid (Editor & coauthor), On Space and Time Cambridge University Press, (2008) 320pp. & paperback (2012). Authors: A. Connes, M. Heller, R. Penrose, J. Polkinghorne, A. Taylor, and me

  5. 5.E.J. Beggs and S. Majid, Quantum Riemannian Geometry, Grundlehren der mathematischen Wissenschaften, vol. 355, Springer (2020) 809pp.


Lecture notes and review articles


  1. 6.S. Majid, Non-commutative-geometric groups by a bicrossproduct construction: Hopf Algebras at the Planck scale. PhD Thesis, Harvard University Archives 1988

  2. 7.S. Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Int. J. Modern Physics A 5(1) (1990) 1-91

  3. 8.S. Majid, Beyond supersymmetry and quantum symmetry (An introduction to braided groups and braided matrices), in M-L. Ge and H.J. de Vega eds., Quantum Groups, Integrable Statistical Models and Knot Theory. World Sci. (1993) 231-282

  4. 9.S. Majid, Algebras and Hopf algebras in braided categories, in Lec. Notes Pure and Applied Maths 158 (1994) 55-105. Marcel Dekker

  5. 10.S. Majid, Introduction to braided geometry and q-Minkowski space, in Proc. School `Enrico Fermi' CXXVII IOS Press, (1996) 267-348

  6. 11.S. Majid, Meaning of noncommutative geometry and the Planck-scale quantum group, Springer Lect. Notes Phys. 541 (2000) 227-276

  7. 12.S. Majid, Quantum groups and noncommutative geometry, J. Math. Phys. (Millenium Volume, by invitation) 41 (2000) 3892-3942

  8. 13.S. Majid, Algebraic approach to quantum gravity III: noncommutative Riemannian geometry, in Mathematical and Physical Aspects of Quantum Gravity, eds. B. Fauser, J. Tolksdorf and E. Zeidler, Birkhauser (2006) 77-100

  9. 14.S. Majid, Algebraic approach to quantum gravity II: noncommutative spacetimes, in Approaches to Quantum Gravity, ed. D. Oriti. C.U.P. (2009) 466-492

  10. 15.S. Majid, Algebraic approach to quantum gravity I: relative realism, Proceedings of Road to Reality with Roger Penrose.,  eds., J. Ladyman et al, Copernicus Center Press (2015) 117-177

  11. 16.S. Majid, Quantum spacetime and physical reality, in On Space and Time, see above, Cambridge Univ. Press (2008)  56-140

  12. 17.S. Majid, Philosophy of space and time, in Unesco-Eolss, (2012)  50pp

  13. 18.S. Majid, Quantum groups and braided algebra, in Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse, eds. C. Heunen, M. Sadrzadeh and E. Grefenstette, Oxford Univ. Press (2013)  90-114

  14. 19.S. Majid, The self-representing Universe, in Mathematical Structures of the Universe, eds. M. Eckstein, M. Heller, S. Szybka, Copernicus Center Press (2014) 357-387

  15. 20.S. Majid, Noncommutative differential geometry, in LTCC Lecture Notes Series: Analysis and Mathematical Physics, eds. S. Bullet, T. Fearn and F. Smith, World Sci. (2017) 139-176

  16. 21.J. Argota-Quiroz and S. Majid, Quantum gravity on finite spacetimes and dynamical mass, Corfu Summer Institute 2021: School and Workshops on Elementary Particle Physics and Gravity, PoS (2022) 210 (41pp)

  17. 22.S. Majid, Algebraic approach to quantum gravity IV: applications, Corfu Summer Institute 2025: School and Workshops on Elementary Particle Physics and Gravity, PoS (2025) xxx (45pp)


Shorter expository articles


  1. 23.S. Majid, Spectrum generating algebras, Kluwer Ency. Math. Supp. I (1997) 456-458

  2. 24.S. Majid, Braided categories; Braided groups; Quasitriangular Hopf algebras (3 articles), Kluwer Ency. Math. Supp. II (2000) 84-87, 87-90, 399-401

  3. 25.S. Majid, Noncommutative geometry and quantum groups, Phil. Trans. Roy. Soc. A 358 (2000) 89-109.

  4. 26.S. Majid, Eight contributions in Concise Ency. Supersymmetry, Kluwer (2003)

  5. 27.S. Majid, Bicrossproduct Hopf algebras and noncommutative spacetime, in Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, (2006)  Vol I, pp. 265-274

  6. 28.S. Majid, Hopf algebras and q-deformation quantum groups, in Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, (2006) Vol II, pp. 687-700

  7. 29.S. Majid, What is a quantum group? Notices of the A.M.S. (by invitation) 53 (2006) 28-29

  8. 30.S. Majid, Quantum groups, in Princeton Companion to Mathematics (by invitation of T. Gowers, editor) (2008) 272-275

  9. 31. S. Majid, Emergence of wave equations from quantum geometry, in Proceedings of the 6th International School on Field Theory and Gravitation, AIP  Conf. Proc. 1483 (2012) 169-188

  10. 32.S. Majid, Emergence of Riemannian geometry and the massive graviton,  Euro Phys. J. Web of Conferences, 71 (2014) 0080 (14pp)

  11. 33.S. Majid, On the emergence of the structure of Physics, Phil. Trans. Roy. Soc. A (2018) 376 20170231 (16pp)


Early physics papers


  1. 34.S. Majid, Canonical arbitrary - spin background - field wave operator. Il Nuov. Cim. 101A (1989) 857-882

  2. 35.S. Majid, Mass dependence of U(1) axial symmetry breakdown, Il Nuov. Cim. 104A (1991) 617-640

  3. 36.S. Majid, Gauge covariant vacuum expectations and glueballs, Il Nuov. Cim. 104A (1991) 949-960

  4. 37.S. Majid, Liouville theorem for the Yang-Mills self-duality equations, J. Math. Phys. 29 (1988) 2303-2310; erratum J. Math. Phys. 30 (1989) 1652

  5. 38.S. Majid, Partial waves for the linearized Yang-Mills equation about a monopole background, J. Math. Phys. 30 (1989) 1150-1157


Early papers on Hopf algebras and the Planck scale


  1. 39.S. Majid, Matched pairs of Lie groups and Hopf algebra bicrossproducts, Nuclear Physics B, Proc. Supl. 6 (1989) 422-424

  2. 40.S. Majid, Hopf algebras for physics at the Planck scale, Classical and Quantum Gravity 5 (1988) 1587-1607

  3. 41.S. Majid, Physics for algebraists: non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra 130 (1990) 17-64

  4. 42.S. Majid, Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations, Pacific J. Math 141 (1990) 311-332

  5. 43.S. Majid, Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and classical Yang-Baxter equations, J. Functional Analysis 95 (1991) 291-319

  6. 44.S. Majid, The principle of representation-theoretic self-duality, Phys. Essays. 4(3) (1991) 395-405

  7. 45.S. Majid, Fourier transforms on A/G and knot invariants, J. Math. Phys. 32 (1990) 924-927


Papers on quasitriangular Hopf algebras


  1. 46.S. Majid, Quantum group duality in vertex models and other results, in ed. L-L. Chau and W. Nahm, Nato-ASI Series B, 245 (1990) 373-386. Plenum

  2. 47.S. Majid, Representation-theoretic rank and double Hopf algebras, Comm. Algebra. 18(11) (1990) 3705-3712

  3. 48.E. Beggs and S. Majid, Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on diff(S^1) and diff(R), Ann. Inst. Henri Poincare 53 (1990) 15-34

  4. 49.S. Majid, More Examples of bicrossproduct and double cross product Hopf algebras, Isr. J. Math. 72 (1990) 133-148

  5. 50.S. Majid, Reconstruction theorems and rational conformal field theories, Int. J. Mod. Phys. A. 6 (1991) 4359-4374

  6. 51.S. Majid, Representations, duals and quantum doubles of monoidal categories, Suppl. Rend. Circ. Mat. Palermo., Series II, 26 (1991) 197-206

  7. 52.S. Majid, Quasi-quantum groups as internal symmetries of topological quantum field theories, Lett. Math. Phys. 22 (1991) 83-90

  8. 53.S. Majid, Tannaka-Krein Theorem for quasiHopf algebras and other results, Contemp. Math. 134 (1992) 219-232

  9. 54.S. Majid, Some physical applications of category theory, in Springer Lec. Notes in Physics 375 (1991) 131-142

  10. 54.S. Majid, Doubles of quasitriangular Hopf algebras, Comm. Algebra. 19 (1991) 3061-3073

  11. 56.S. Majid, On q-regularization, Int. J. Modern Physics A. 5 (1990) 4689-4696

  12. 57.S. Majid, Quantum groups and quantum probability, in Quantum Probability and Related Topics VI (1991) 338-358. World Sci.

  13. 58.S. Majid and Ya. S. Soibelman, Chern-Simons theory, modular functions and quantum mechanics in an alcove, Int. J. Mod. Phys. A. 6 (1991) 1815-1827

  14. 59.S. Majid and Ya. S. Soibelman, Rank of quantized universal enveloping algebras and modular functions, Comm. Math. Phys. 137 (1991) 249-262

  15. 60.S. Majid and Ya. S. Soibelman, Bicrossproduct structure of the quantum Weyl group, J. Algebra 163 (1994) 68-87

  16. 61.S. Majid, An open problem in quantum groups, in Springer Lec. Notes in Math 1510 (1992) 391-392


Papers on Hopf algebras in braided categories


  1. 62.S. Majid, Braided groups and algebraic quantum field theories, Lett. Math. Phys. 22 (1991) 167-176

  2. 63.S. Majid, Examples of braided groups and braided matrices, J. Math. Phys. 32 (1991) 3246-3253

  3. 64.S. Majid, Rank of quantum groups and braided groups in dual form, in Springer Lec. Notes in Math 1510 (1992) 79-88

  4. 65.A. J. Macfarlane and S. Majid, Quantum group structure in a fermionic extension of the quantum harmonic oscillator, Phys. Lett. B. 268 (1991) 71-74

  5. 66.A. J. Macfarlane and S. Majid, The superalgebra osp(1|2) and a related quantum group for harmonic oscillator systems, in Proc. Topological and Geometrical Methods in Field Theory , Turku, Finland. World Sci. (1992) 227-236

  6. 67.A. J. Macfarlane and S. Majid, Spectrum generating quantum group of the harmonic oscillator, Int. J. Mod. Phys. A. 7(18) (1992) 4377-4393

  7. 68.S. Majid, Braided groups, J. Pure Applied Algebra 86 (1993) 187-221

  8. 69.S. Majid, Transmutation theory and rank for quantum braided groups, Math. Proc. Camb. Phil. Soc. 113 (1993) 45-70

  9. 70.S. Majid, Cross products by braided groups and bosonization, J. Algebra 163 (1994) 165-190

  10. 71.S. Majid, Braided groups and braid statistics, in Quantum Probability and Related Topics VIII (1992) 281-295. World Sci.

  11. 72.S. Majid, Anyonic quantum groups, in Z. Oziewicz at al, eds., Spinors, Twistors, Clifford Algebras and Quantum Deformations. Kluwer (1993) 327-336

  12. 73.V. Lyubashenko and S. Majid, Braided groups and quantum Fourier transform, J. Algebra. 166 (1994) 506-528

  13. 74.V. Lyubashenko and S. Majid, Fourier transform identities in quantum mechanics and the quantum line, Phys. Lett. B. 284 (1992) 66-70

  14. 75.S. Majid, C-statistical Quantum Groups and Weyl Algebras, J. Math. Phys. 33 (1992) 3431-3444

  15. 76.J. Donin, D. Gurevich and S. Majid, R-matrix brackets and their quantization, Ann. Inst. H. Poincare 58 (1993) 235-246

  16. 77.D. Gurevich and S. Majid, Braided groups of Hopf algebras obtained by twisting, Pac. J. Math. 162 (1994) 27-44

  17. 78.S. Majid and M. J. Rodriguez-Plaza, Quantum and super-quantum group related to the Alexander-Conway polynomial, J. Geom. Physics 11 (1993) 437-443

  18. 79.S. Majid and M. J. Rodriguez-Plaza, Nonstandard quantum groups and superisation, J. Math. Phys. 36 (1995) 7071-7097

  19. 80.S. Majid, Braided groups and duals of monoidal categories, Can. Math. Soc. Conf. Proc., 13 (1992) 329-343

  20. 81.S. Majid, Quantum and braided linear algebra, J. Math. Phys. 34 (1993) 1176-1196

  21. 82.S. Majid, Infinite braided tensor products and 2D quantum gravity, Int. J. Mod. Phys A (Proc. Suppl.) 3A (1993) 294-297

  22. 83.W.K. Baskerville and S. Majid, Braided and unbraided harmonic oscillators, Anales de Fisica, Monografias, 1 (1993) 61-64. CIEMAT/RSEF, Madrid

  23. 84.W.K. Baskerville and S. Majid, The braided Heisenberg group, J. Math. Phys. 34 (1993) 3588-3606

  24. 85.S. Majid, Quantum double as quantum mechanics, J. Geom. Phys. 13 (1994) 169-202

  25. 86.S. Majid, Braided momentum in the q-Poincare group, J. Math. Phys. 34 (1993) 2045-2058

  26. 87.S. Majid, Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group, Comm. Math. Phys. 156(1993) 607-638

  27. 88.S. Majid, Free braided differential calculus, braided binomial theorem and the braided exponential Map, J. Math. Phys. 34 (1993) 4843-4856

  28. 89.S. Majid, Quantum and braided Lie-algebras, J. Geom. Phys. 13 (1994) 307-356

  29. 90.S. Majid and M. Markl, Glueing operation for R-matrices, quantum groups and link invariants of Hecke type, Math. Proc. Camb. Phil. Soc. 119 (1995) 139-166

  30. 91.S. Majid, Braided geometry: a new approach to q-deformations, in R. Coquereaux et al, eds., First Caribbean Spring School of Mathematics and Theoretical Physics. World Sci. (1995) 190-204

  31. 92.S. Majid and M. J. Rodriguez-Plaza, Random walks and the heat equation on superspace and anyspace J. Math. Phys. 35 (1994) 3753-3769

  32. 93.S. Majid, On the addition of quantum matrices, J. Math. Phys. 35 (1994) 2617-2632

  33. 94.S. Majid, Lie algebras and braided geometry, Adv. Appl. Cliff. Algebras (Proc. Suppl.) 4 61-77 (1994)

  34. 95.S. Majid and U. Meyer, Braided matrix structure of q-Minkowski space and q-Poincare group, Z. Phys. C. 63 (1994) 357-362

  35. 96.S. Majid, Solutions of the Yang-Baxter equations from braided-Lie algebras and braided groups, J. Knot Th. Ramif. 4 (1995) 673-697

  36. 97.S. Majid, q-Euclidean space and quantum Wick rotation by twisting, J. Math. Phys. 35 (1994) 5025-5033

  37. 98.A. Kempf and S. Majid, Algebraic q-integration and Fourier theory on quantum and braided spaces, J. Math. Phys. 35 (1994) 6802-6837

  38. 99.S. Majid, q-Epsilon tensor on quantum and braided spaces, J. Math. Phys. 36 (1995) 1991-2007

  39. 100.S. Majid, *-Structures on braided spaces, J. Math. Phys. 36 (1995) 4436-4449

  40. 101.S. Majid, Braided approach to exterior algebra on q-Euclidean and q-Minkowski spaces, in J. Lukierski et al, eds., Quantum Groups: Proc. 30th Winter School of Theoretical Physics, Karpacz. Polish Sci. (1994) 131-148

  41. 102.S. Majid and M. J. Rodriguez-Plaza, Anyonic FRT construction, Czech. J. Phys. 44 (1994) 1073-1080.

  42. 103.S. Majid, Some remarks on the q-Poincare algebra in R-matrix form, in H.-D. Doebner et al., eds., Proc. Nonlinear, Deformed and Irreversible Quantum Systems, World Sci. (1995) 352-384

  43. 104.S. Majid, Quasi-* structure on q-Poinare algebras, J. Geom. Phys. 22 (1997) 14-58

  44. 105.S. Majid, Diagrammatics of braided group gauge theory, J. Knot Th. Ramif. 8 (1999) 731-771

  45. 106.S. Majid, Some comments on bosonisation and biproducts, Czech J. Phys. 47 (1997) 151-172

  46. 107.S. Majid, Double bosonisation of braided groups and the construction of U_q(g), Math. Proc. Camb. Phil. Soc.125 (1999) 151-192

  47. 108.S. Majid, Braided geometry of the conformal algebra, J. Math. Phys. 37 (1996) 6495-6509

  48. 109.S. Majid, Braided geometry and the inductive construction of Lie algebras and quantum groups, in S. Gutt et al., eds., Deformation Theory and Symplectic Geometry. Kluwer (1997) 339-344

  49. 110. S. Majid, New quantum groups by double-bosonisation, Czech J. Phys. 47 (1997) 79-90

  50. 111. S. Majid, Anyonic Lie algebras, Czech J. Phys. 47 (1997) 1241-1249

  51. 112. S. Majid, Some remarks on braided reconstruction and the braided double, Czech J. Phys. 48 (1998) 1447-1456

  52. 113. H. Albuquerque and S. Majid, Quasialgebra structure of the octonions, J. Algebra 220 (1999) 188-224

  53. 114. H. Albuquerque and S. Majid, Z_n-Quasialgebras Textos de Mat. de Coimbra Ser. B 19 (1999) 57-64

  54. 115. H. Albuquerque and S. Majid, New approach to the octonions and cayley algebras, in Lec. Notes Pure and Applied Maths 211 (2000) 1-7. Marcel Dekker

  55. 116. S. Majid, Braided-Lie Bialgebras, Pac. J. Math. 192 (2000) 329-356

  56. 117. H. Albuquerque and S. Majid, Clifford algebras obtained by twisting of group algebras, J. Pure Applied Algebra 171 (2002) 133-148

  57. 118. P.J. Cameron and S. Majid, Braided line and counting fixed points of GL(d,F_q), Commun. Algebra 31 (2003) 2003-2013

  58. 119. G.A. Goldin and S. Majid, On the Fock space for nonrelativistic anyon fields and braided tensor products, J. Math. Phys. 45 (2004) 3770-3787

  59. 120. S.E. Akrami and S. Majid, Braided cyclic cocycles and nonassociative geometry, J. Math. Phys. 45 (2004) 3883-3911

  60. 121. S. Majid, Gauge theory on nonassociative spaces, J. Math. Phys. 46 (2005) 103519, 23pp.

  61. 122. J. Klim and S. Majid, Hopf quasigroups and the algebraic 7-sphere, J. Algebra, 323 (2010) 3067-3110

  62. 123. J. Klim and S. Majid, Bicrossproduct Hopf quasigroups, Comm. Math. U. Carolinas, 51 (2010) 287-304

  63. 124. S. Majid and I. Tomasic, On braided zeta functions, Bull. Math.Sci., 1 (2011) 379-396

  64. 125. J. Lopez Pena, S. Majid and K. Rietsch, Lie theory of finite simple groups and the Roth property, Math. Proc. Camb. Phil. Soc., 163 (2017) 301-340


Papers on quantum geometry


  1. 126. S. Majid, On Hopf algebra duality in quantum systems, Anales de Fisica, Monografias, 1 (1993) 145-148

  2. 127. T. Brzezinski and S. Majid, Quantum group gauge theory and q-monopoles, Anales de Fisica, Monografias, 1 (1993) 75-58

  3. 128. T. Brzezinski and S. Majid, Quantum group gauge theory on classical spaces, Phys. Lett. B. 298 (1993) 339-343

  4. 129. T. Brzezinski and S. Majid, A class of bicovariant differential calculi on Hopf algebras, Lett. Math. Phys. 26 (1992) 67-78

  5. 130. S. Majid, Quantum random walks and time-reversal, Int. J. Mod. Phys. A. 8 (1993) 4521-4545

  6. 131. T. Brzezinski and S. Majid, Quantum group gauge theory on quantum spaces, Comm. Math. Phys. 157 (1993) 591-638

  7. 132. S. Majid, Cross product quantisation, nonAbelian cohomology and twisting of Hopf algebras, in H.-D. Doebner, V.K. Dobrev & A.G. Ushveridze, eds., Generalized symmetries in Physics. World Sci. (1994) 13-41

  8. 133. S. Majid and H. Ruegg, Bicrossproduct structure of the k-Poincare group and non-commutative geometry, Phys. Lett. B. 334 (1994) 348-354

  9. 134. S. Majid, Some remarks on the quantum double, Czech. J. Phys. 44 (1994) 1059-1071.

  10. 135. S. Majid, Duality principle and braided geometry, in Springer Lect. Notes Phys. 447 (1995) 125-144

  11. 136. E. Beggs, J. Gould and S. Majid, Finite group factorisations and braiding J. Algebra 181 (1996) 112-151

  12. 137. S. Majid, Bicrossproduct structure of affine quantum groups, Lett. Math. Phys. 39 (1997) 243-252

  13. 138. S. Majid, Some remarks on quantum and braided group gauge theory, Banach Center Publications 40 (1997) 335-349

  14. 139. S. Majid, Fermionic q-Fock space and braided geometry, J. Math. Phys. 38 (1997) 4845-4853

  15. 140. S. Majid, Advances in quantum and braided geometry, in H.-D. Doebner & V.K. Dobrev, eds., Quantum Group Symposium at Group XXI, Heron Press, Sofia (1997) 11-26

  16. 141. S. Majid, Quantum geometry and the Planck scale, in H.-D. Doebner, W. Scherer & P. Nattermann, eds., Group XXI Physical Applications and Mathematical Aspects of Geometry, Groups, and Algebras, World Sci. (1997) 275-284

  17. 142. S. Majid, Classification of bicovariant differential calculi, J. Geom. Phys. 25 (1998) 119-140

  18. 143. T. Brzezinski and S. Majid, Coalgebra bundles, Commun. Math. Phys. 191 (1998) 467-492

  19. 144. S. Majid, Quantum double of quasi-Hopf algebras, Lett. Math. Phys. 45 (1998) 1-9.

  20. 145. S. Majid, Quantum and braided diffeomorphism groups, J. Geom. Phys. 28 (1998) 94-128

  21. 146. T. Brzezinski and S. Majid, Line bundles on quantum spheres, in J. Rembielinski, ed., Proc. Particles, Fields and Gravitation, AIP New York (1998) 3-8

  22. 147. T. Brzezinski and S. Majid, Quantum differentials and the q-monopole revisited, Acta Appl. Math. 54 (1998) 185-232

  23. 148. S. Majid, Quantum geometry of field extensions, J. Math. Phys. 40 (1999) 2311-2323.

  24. 149. E. Beggs and S. Majid, Quasitriangular and differential structures on bicrossproduct Hopf algebras, J. Algebra 219 (1999) 682-727

  25. 150. S. Majid, Quantum and braided group Riemannian geometry, J. Geom. Phys. 30 (1999) 113-146

  26. 151. P. Hajac and S. Majid, Projective module description of the q-monopole, Commun. Math. Phys. 206 (1999) 246-264

  27. 152. S. Majid and R. Oeckl, Twisting of quantum differentials and the Planck scale Hopf algebra, Commun. Math. Phys. 205 (1999) 617-655

  28. 153. S. Majid and R. Oeckl, Twisting of quantum differentials, in Springer Lect. Notes Phys. 543 (2000) 392

  29. 154. G. Amelino-Camelia and S. Majid, Waves on noncommutative spacetime and gamma-ray bursts, Int. J. Mod. Phys. A 15 (2000) 4301-4323

  30. 155. S. Majid, Conceptual issues for noncommutative gravity on algebras and finite sets, Int. J. Mod. Phys. B 14 (2000) 2427-2449

  31. 156. T. Brzezinski and S. Majid, Quantum geometry of algebra factorisations and coalgebra bundles, Commun. Math. Phys.213 (2000) 491-521

  32. 157. E.J. Beggs and S. Majid, Poisson-Lie T-duality for quasitriangular Lie bialgebras, Commun. Math. Phys. 220 (2001) 455-488

  33. 158. S. Majid, Noncommutative differential geometry and twisting of quantum groups, in L.M.S. Lect. Notes 290 (2001) 175-190

  34. 159. S. Majid, Riemannian geometry of quantum groups and finite groups with nonuniversal differentials, Commun. Math. Phys. 225 (2002) 131-170

  35. 160. S. Majid, Classification of differentials on quantum doubles and finite noncommutative geometry, Lect. Notes Pure Appl. Maths 239 (2004) 167-188, Marcel Dekker

  36. 161. S. Majid and T. Schucker, Z_2 x Z_2 lattice as a Connes-Lott-quantum group model, J. Geom. Phys. 43 (2002) 1-26

  37. 162. F. Ngakeu, S. Majid and D. Lambert, Noncommutative Riemannian geometry of the alternating group A_4, J. Geom. Phys. 42 (2002) 259-282

  38. 163. S. Majid and E. Raineri, Electromagnetism and gauge theory on the permutation group S_3, J. Geom. Phys. 44 (2002) 129-155

  39. 164. S. Majid, Noncommutative differentials and Yang-Mills on permutation groups S_N, Lect. Notes Pure Appl. Maths 239 (2004) 189-214, Marcel Dekker

  40. 165. F. Ngakeu, S. Majid and J-P. Ezin, Classification of differentials and Cartan calculus on bicrossproducts, Acta. Applic. Math. 84 (2004) 193-236

  41. 166. X. Gomez and S.Majid, Noncommutative cohomology and electromagnetism on Cq[SL2] at roots of unity, Lett. Math. Phys. 60 (2002) 221-237

  42. 167. S.Majid,  Noncommutative Ricci curvature and Dirac operator on Cq[SL2] at roots of unity, Lett. Math. Phys. 63 (2003) 39-54

  43. 168. E. Batista and S. Majid, Noncommutative geometry on the algebra U(su_2) and quantization of coadjoint orbits, in Group 24: Physical and Mathematical Aspects of Symmetries , eds. J-P. Gazeau et al, IOP (2003), 4 pp

  44. 169. S. Majid, Noncommutative physics on Lie algebras, Z_2^n lattices and Clifford algebras, in Clifford Algebras: Application to Mathematics, Physics, and Engineering, ed. R. Ablamowicz, Birkhauser (2003) pp. 491-518

  45. 170. E. Batista and S. Majid, Noncommutative geometry of angular momentum space U(su_2), J. Math. Phys. 44 (2003) 107-137

  46. 171. X. Gomez and S.Majid, Relating quantum and braided Lie algebras, Banch Center Publications  61 (2003) 91-102

  47. 172. X. Gomez and S.Majid, Braided Lie algebras and bicovariant differential calculi over coquasitriangular Hopf algebras, J. Algebra 261 (2003) 334-388

  48. 173. S. Majid and E. Raineri, Moduli of quantum Riemannian geometries on <= 4 points, J. Math. Phys. 45 (2004) 4596-4627

  49. 174. S. Majid, Noncommutative Riemannian and spin geometry of the standard q-sphere, Commun. Math. Phys. 256 (2005) 255-285

  50. 175. E.J. Beggs and S. Majid, Semiclassical differential structures, Pac. J. Math. 224 (2006) 1-44

  51. 176. S. Majid, Noncommutative model with spontaneous time generation and Planckian bound, J. Math. Phys. 46 (2005) 103520, 18 pp

  52. 177. T. Hadfield and S. Majid, Bicrossproduct approach to the Connes-Moscovici Hopf algebra, J. Algebra 312 (2007) 228-256

  53. 178. T. Gateva-Ivanova and S. Majid, Matched pairs approach to set theoretic solutions of the Yang-Baxter equations, J. Algebra 319 (2008) 1462-1529

  54. 179. T. Gateva-Ivanova and S. Majid, Set theoretic solutions of the Yang-Baxter equations, graphs and computations, J. Symb. Comp. 42 (2007) 1079-1112

  55. 180. L. Freidel and S. Majid, Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity, Class. Quant. Gravity 25 (2008) 045006 (37pp)

  56. 181. S. Brain and S. Majid, Quantisation of twistor theory by cocycle twist, Commun. Math. Phys. 284 (2008) 713-774

  57. 182. E.J. Beggs and S. Majid, Bar categories and star operations, Alg. and Representation Theory 12 (2009) 103-152

  58. 183. S. Majid and B. Schroers, q-Deformation and semidualisation in 3D quantum gravity, J. Phys A 42 (2009) 425402 (40pp)

  59. 184. T. Gateva-Ivanova and S. Majid, Quantum spaces associated to multipermutation solutions of level two, Alg. and Representation Theory, 14 (2011) 341-376

  60. 185. E.J. Beggs and S. Majid, Quantization by cochain twists and nonassociative differentials,  J. Math. Phys., 51 (2010) 053522, 32pp

  61. 186. E.J. Beggs and S. Majid, *-Compatible connections in noncommutative Riemannian geometry, J. Geom. Phys. 61 (2011) 95-124

  62. 187. E.J. Beggs and S. Majid, Nonassociative Riemannian geometry by twisting,  J. Phys. Conf. Ser. 254 (2010) 012002 (29pp)

  63. 188. S. Majid, Scaling limit of the noncommutative black hole,  J. Phys. Conf. Ser. 284 (2011) 012003 (12pp)

  64. 189. S. Majid, q-Fuzzy spheres and quantum differentials on B_q[SU_2] and U_q(su_2), Lett. Math. Phys. 98 (2011) 167-191

  65. 190. S. Majid, Almost commutative Riemannian geometry: wave operators, Commun. Math. Phys. 310 (2012) 569-609

  66. 191. S. Majid, Noncommutative Riemannian geometry of graphs, J. Geom. Phys. 69 (2013) 74-93

  67. 192. S. Majid and K. Rietsch, Lie theory and coverings of finite groups, J. Algebra, 389 (2013) 137-150

  68. 193. S. Majid, Newtonian gravity on quantum spacetime,  Euro Phys. J. Web of Conferences, 70 (2014) 00082 (10pp)

  69. 194. E.J. Beggs and S. Majid, Gravity induced from quantum spacetime, Class. Quantum. Grav. 31 (2014) 035020 (39pp)

  70. 195. S. Majid and W.-Q. Tao, Duality for generalised differentials on quantum groups, J. Algebra 439 (2015) 67-109

  71. 196. S. Majid and W.-Q. Tao, Cosmological constant from quantum spacetime, Phys. Rev. D  91 (2015)  124028 (12pp)

  72. 197. S. Majid and W.-Q. Tao, Noncommutative differentials on Poisson-Lie groups and pre-Lie algebras, Pac. J. Math. 284 (2016) 213-256

  73. 198. E.J. Beggs and S. Majid, Spectral triples from bimodule connections and Chern connections, J. Noncomm. Geom., 11 (2017) 669-701

  74. 199. E.J. Beggs and S. Majid, Quantum Riemannian geometry of phase space and nonassociativity, Demonstratio Math., 50 (2017) 83-93

  75. 200. S. Majid, Hodge star as braided Fourier transform, Alg. Repn. Theory, 20 (2017) 695-733

  76. 201. E.J. Beggs and S. Majid, Poisson-Riemannian geometry, J. Geom. Phys.  114 (2017) 450-491

  77. 202. S. Majid, Strict quantum 2-groups, 20pp. arXiv:1208.6265 (math.QA)

  78. 203. S. Majid, Reconstruction and quantization of Riemannian structures, J. Math. Phys.  61 (2020) 022501 (32pp) Editor's pick award

  79. 204. M.E. Bassett and S. Majid, Finite noncommutative geometries related to F_p[x],  Alg. Repn. Theory, 23 (2020) 251-274

  80. 205. C. Fritz and S. Majid, Noncommutative spherically symmetric spacetimes at semiclassical order, Class. Quantum Grav, 34 (2017) 135013 (50pp)

  81. 206. S. Majid and W.-Q. Tao, Generalised noncommutative geometry on finite groups and Hopf quivers, J. Noncomm. Geom. 13 (2019) 1055-1116

  82. 207. S. Majid and A. Pachol, Classification of digital affine noncommutative geometries, J. Math. Phys. 59(2018) 033505 (30pp)

  83. 208. R. Aziz and S. Majid, Codouble bosonisation and dual bases of c_q[SL_2] and c_q[SL_3], J. Algebra 518 (2019) 75-118

  84. 209. E.J. Beggs and S. Majid, Quantum Bianchi identities and characteristic classes via DG categories, J. Geom. Phys. 124 (2018) 350-370

  85. 210. R. Akylzhanov, S. Majid and M. Ruzhansky, Smooth dense subalgebras and Fourier multipliers on compact quantum groups, Commun. Math. Phys. 362 (2018) 761-799

  86. 211. S. Majid and L. Williams, Quantum Koszul formula on quantum spacetime, J. Geom. Phys. 129 (2018) 41-69

  87. 212. S. Majid and P.K. Osei, Quasitriangular structure and twisting of the 2+1 bicrossproduct model, J. High Energ. Phys. 1 (2018) 147 (28pp)

  88. 213. S. Majid and A. Pachol, Digital finite quantum Riemannian geometries, J. Phys. A 53 (2020) 115202 (40pp)

  89. 214. S. Majid, Quantum gravity on a square graph, Class. Quantum Grav 36 (2019) 245009 (23pp)

  90. 215. S. Majid, Quantum Riemannian geometry and particle creation on the integer line, Class. Quantum Grav 36 (2019) 135011 (22pp)

  91. 216. S. Majid and L. Williams, Poisson principal bundles, SIGMA 17 (2021) 006, 23pp

  92. 217. R. Aziz and S. Majid, Quantum differentials on cross product Hopf algebras, J. Algebra 531 (2020) 303-351

  93. 218. S. Majid, Quantum geometry of Boolean algebras and de Morgan duality, J. Noncomm. Geom. 17 (2023) 37-79

  94. 219. E.J. Beggs and S. Majid, Quantum geodesics in quantum mechanics, J. Math. Phys. 65 (2024) 012101 (37pp)

  95. 220. S. Majid, Quantum geometry, logic and probability, Phil. Prob. Sci. (Zag. Fil. Nauce) 69 (2020) 191-236

  96. 221. E. Lira-Torres and S. Majid, Quantum gravity and Riemannian geometry on the fuzzy sphere, Lett. Math. Phys. (2021) 111:29 (21pp)

  97. 222. J. Argota-Quiroz and S. Majid, Quantum gravity on polygons and R x Z_n FLRW model, Class. Quantum Grav. 37 (2020) 245001 (43pp)

  98. 223. S. Majid and A. Pachol, Digital quantum groups, J. Math. Phys. 61 (2020) 103510 (34pp)

  99. 224. J. Argota-Quiroz and S. Majid, Fuzzy and discrete black hole models, Class. Quantum Grav. 38 (2021) 145020 (36pp)

  100. 225. E. Lira-Torres and S. Majid, Geometric Dirac operator on the fuzzy sphere, Lett. Math. Phys. (2022) 112:10 (22pp)

  101. 226. C. Liu and S. Majid, Quantum geodesics on quantum Minkowski spacetime, J. Phys. A 55 (2022) 424003 (35pp)

  102. 227. E. Beggs and S. Majid, Quantum geodesic flows and curvature, Lett. Math. Phys.(2023) 113:73 (44pp)

  103. 228. S. Majid and F. Simao, Quantum jet bundles, Lett. Math. Phys.(2023) 113:120 (60pp)

  104. 229. J. Argota-Quiroz and S. Majid, Quantum Riemannian geometry of the discrete interval and q-deformation, J. Math. Phys. 64 (2023) 051701 Editor's pick award

  105. 230. X. Han and S. Majid, Hopf-Galois extensions and twisted Hopf algebroids, J. Algebra 641 (2024) 754-794

  106. 231. E. Lira-Torres and S. Majid, Geometric Dirac operator on noncommutative torus and M_2(C) Lett. Math. Phys. 114 (2024) 70 (41pp)

  107. 232. S. Majid, Dirac operator associated to a quantum metric, J. Noncomm. Geom. 19 (2025) 573-600 (28pp)

  108. 233. C. Liu and S. Majid, Quantum Kaluza-Klein theory with M_2(C), J. High Energ. Phys. (2023) 102 (33pp)

  109. 234. X. Han and S. Majid, Bisections and cocycles on Hopf algebroids, in press J. Noncomm. Geom. (2026)

  110. 235. T. Gateva-Ivanova and S. Majid, Quadratic algebras and idempotent braided sets, arXiv:2409.02939 (math.QA)

  111. 236. E.J. Beggs and S. Majid, Quantum geodesic flow on the integer lattice line, J. Phys. Conf. Ser. 2667 (2023) 012016

  112. 237. C. Liu and S. Majid, Yang-Mills fields from fuzzy sphere quantum Kaluza-Klein model, J. High Energ. Phys. 07 (2024) 195

  113. 238. E. Beggs and S. Majid, Quantum geodesic flows on graphs, Lett. Math. Phys. (2024) 114:112 (41pp)

  114. 239. S. Majid, Quantum gravity:are we there yet? Phil. Trans. Roy. Soc. A 383 (2025) 20230377 (20pp)

  115. 240. S. Blitz and S. Majid, Quantum curvature fluctuations and the cosmological constant in a single plaquette quantum gravity model, Class. Quantum Grav. Lett. 42 (2025) 04LT01 (12pp)

  116. 241. S. Majid and L.S. McCormack, Quantum geometric Wigner construction for D(G) and braided racks, J. Math. Phys. 66 (2025) 061701 (59pp)

  117. 242. E. Beggs and S. Majid, Complex structure on quantum-braided planes, Lett. Math. Phys. (2025) 115:29 (36pp)

  118. 243. C. Liu and S. Majid, Fermions in the fuzzy sphere Kaluza-Klein model, J. Math. Phys. 66 (2025) 112301 (15pp)

  119. 244. E. Beggs and S. Majid, Generally covariant quantum mechanics, Lett. Math. Phys. 116 (2026) 9 (65pp)

  120. 245. E. Beggs, X. Han and S. Majid, *-Hopf algebroids, arXiv: 2412.21089 (math.QA)

  121. 246. E. Beggs and S. Majid, Klein-Gordon flow on FLRW spacetimes, arXiv: 2501.18295 (gr-qc)

  122. 247. S. Majid and F. Simao, Finite group gauge theory on graphs and gravity-like modes, Nucl. Phys. B 1020 (2025) 117117 (38pp)

  123. 248. X. Han and S. Majid, Quantum jet Hopf algebroids by cotwist, arXiv: 2507.02848 (math.QA)

  124. 249. C. Liu and S. Majid, Kaluza-Klein ansatz from Lorentzian quantum gravity on the fuzzy sphere,Euro. Phys. Jour. C 85: (2025) 1464 (12pp)

  125. 250. S. Majid and F. Simao, Quantum variational calculus on a lattice, arXiv: 2508.02628 (hep-th)

  126. 251. K. Kumar and S. Majid, Geodesic flows on a black-hole background, arXiv: 2603.03222 (gr-qc)

  127. 252. S. Majid, Time-slicing quantum spacetimes, arXiv: 2605.00520 (gr-qc)

  128. 253. K. Kumar and S. Majid, Geometric Aharonov-Bohm phase effect around a black hole, arXiv: 2605.28582 (gr-qc)


Papers on quantum computing


  1. 254. S. Majid, Quantum and braided ZX calculus, J. Phys. A 55 (2022) 254007 (35pp)

  2. 255. A. Cowtan and S. Majid, Quantum double aspects of surface code models, J. Math. Phys. 63 (2022) 042202 (49pp)

  3. 256. S. Majid and K. Rietsch, Planar spider theorem and asymmetric Frobenius algebras, arXiv: 2109.12106 (math.QA)

  4. 257. A. Cowtan and S. Majid, Algebraic aspects of boundaries in the Kitaev quantum double model, J. Math. Phys. 64 (2023) 051701 (60pp)



Book reviews


  1. 1. S. Majid, Book Review of "Multidimensional Hypergeometric Functions and Representations of Lie Algebras and Quantum Groups by A. Varchenko", Bull. London Math. Soc. 29 (1997) 759-761

  2. 2. S. Majid, Book Review of "Knots and Feynman Diagrams by D. Kreimer", Math. Gazette 86 (2002) 155

My Recent arXiv Preprints with Abstractshttp://arxiv.org/a/majid_s_1.html
My arXiv Preprints since June 1992 http://arxiv.org/find/all/1/all:+AND+Shahn+Majid/0/1/0/all/0/1
Google Scholar Citations http://scholar.google.co.uk/citations?user=Ax2xgpIAAAAJ&hl=en