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Volumn 41, Issue 6, 2000, Pages 3892-3942

Quantum groups and noncommutative geometry

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EID: 0034386619     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533331     Document Type: Article
Times cited : (56)

References (73)
  • 1
    • 0040602617 scopus 로고
    • Principle of representation-theoretic self-duality
    • S. Majid, "Principle of representation-theoretic self-duality," Phys. Essays 4(3), 395-405 (1991).
    • (1991) Phys. Essays , vol.4 , Issue.3 , pp. 395-405
    • Majid, S.1
  • 2
    • 0002293135 scopus 로고
    • Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices)
    • edited by M-L. Ge and H. J. de Vega World Scientific Singapore
    • S. Majid, "Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices)," in Quantum Groups, Integrable Statistical Models and Knot Theory, edited by M-L. Ge and H. J. de Vega (World Scientific Singapore, 1993), pp. 231-282.
    • (1993) Quantum Groups, Integrable Statistical Models and Knot Theory , pp. 231-282
    • Majid, S.1
  • 3
    • 0040654365 scopus 로고    scopus 로고
    • Introduction to braided geometry and q-Minkowski space
    • edited by L. Castellani and J. Wess IOS, Amsterdam
    • S. Majid, "Introduction to braided geometry and q-Minkowski space," in Proceedings of the International School 'Enrico Fermi' CXXVII edited by L. Castellani and J. Wess (IOS, Amsterdam, 1996), pp. 267-348.
    • (1996) Proceedings of the International School 'Enrico Fermi' CXXVII , pp. 267-348
    • Majid, S.1
  • 4
    • 0000481618 scopus 로고
    • Quantum groups
    • edited by A. Gleason AMS, Providence, RI
    • V. G. Drinfeld, "Quantum groups," in Proceedings of the ICM, edited by A. Gleason (AMS, Providence, RI, 1987) pp. 798-820.
    • (1987) Proceedings of the ICM , pp. 798-820
    • Drinfeld, V.G.1
  • 5
    • 0040323775 scopus 로고
    • A q-difference analog of U(g) and the Yang-Baxter equation
    • M. Jimbo, "A q-difference analog of U(g) and the Yang-Baxter equation," Lett. Math. Phys. 10, 63-69 (1985).
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63-69
    • Jimbo, M.1
  • 6
    • 36149030193 scopus 로고
    • Hopf algebras for physics at the Planck scale
    • S. Majid, "Hopf algebras for physics at the Planck scale," J. Classical Quantum Gravity 5, 1587-1606 (1988).
    • (1988) J. Classical Quantum Gravity , vol.5 , pp. 1587-1606
    • Majid, S.1
  • 8
    • 84908807046 scopus 로고
    • Examples of braided groups and braided matrices
    • S. Majid, "Examples of braided groups and braided matrices," J. Math. Phys. 32, 3246-3253 (1991).
    • (1991) J. Math. Phys. , vol.32 , pp. 3246-3253
    • Majid, S.1
  • 9
  • 10
    • 0000124925 scopus 로고
    • On q-regularization
    • S. Majid, "On q-regularization," Int. J. Mod. Phys. A 5(24), 4689-4696 (1990).
    • (1990) Int. J. Mod. Phys. A , vol.5 , Issue.24 , pp. 4689-4696
    • Majid, S.1
  • 11
    • 0000776222 scopus 로고
    • Bicrossproduct structure of the K-Poincaré group and noncommutative geometry
    • S. Majid and H. Ruegg, "Bicrossproduct structure of the K-Poincaré group and noncommutative geometry," Phys. Lett. B 334, 348-354 (1994).
    • (1994) Phys. Lett. B , vol.334 , pp. 348-354
    • Majid, S.1    Ruegg, H.2
  • 13
    • 0001534815 scopus 로고
    • Yang-Mills theory over quantum tori
    • A. Connes and M. Rieffel, "Yang-Mills theory over quantum tori," Contemp. Math. 62, 237 (1987).
    • (1987) Contemp. Math. , vol.62 , pp. 237
    • Connes, A.1    Rieffel, M.2
  • 15
    • 0346111908 scopus 로고    scopus 로고
    • Noncommutative geometry and quantum groups
    • S. Majid, "Noncommutative geometry and quantum groups," Philos Trans. R. Soc. A 358, 89-109 (2000).
    • (2000) Philos Trans. R. Soc. A , vol.358 , pp. 89-109
    • Majid, S.1
  • 16
    • 0039417124 scopus 로고    scopus 로고
    • Meaning of noncommutative geometry and the Planck-scale quantum group
    • in press
    • S. Majid, "Meaning of noncommutative geometry and the Planck-scale quantum group," Lect. Notes Phys. (2000) (in press).
    • (2000) Lect. Notes Phys.
    • Majid, S.1
  • 17
    • 0009104514 scopus 로고
    • Duality principle and braided geometry
    • S. Majid, "Duality principle and braided geometry," Lect. Notes Phys. 447, 125-144 (1995).
    • (1995) Lect. Notes Phys. , vol.447 , pp. 125-144
    • Majid, S.1
  • 18
    • 0002036064 scopus 로고
    • Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction
    • S. Majid, "Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction," J. Algebra 130, 17-64 (1990).
    • (1990) J. Algebra , vol.130 , pp. 17-64
    • Majid, S.1
  • 21
    • 0033245408 scopus 로고    scopus 로고
    • Twisting of quantum differentials and the planck scale hopf algebra
    • S. Majid and R. Oeckl, "Twisting of quantum differentials and the Planck scale Hopf algebra," Commun. Math. Phys. 205, 617-655 (1999).
    • (1999) Commun. Math. Phys. , vol.205 , pp. 617-655
    • Majid, S.1    Oeckl, R.2
  • 22
    • 0032274690 scopus 로고
    • K-deformed covariant phase space and quantum gravity uncertainty relations
    • G. Amelino-Camelia, J. Lukierski, and A. Nowicki, "K-deformed covariant phase space and quantum gravity uncertainty relations," Phys. At. Nucl. 61, 1811-1815 (1988).
    • (1988) Phys. At. Nucl. , vol.61 , pp. 1811-1815
    • Amelino-Camelia, G.1    Lukierski, J.2    Nowicki, A.3
  • 24
    • 0039035914 scopus 로고
    • Fourier transforms on AIG and knot invariants
    • S. Majid, "Fourier transforms on AIG and knot invariants," J. Math. Phys. 32, 924-927 (1990).
    • (1990) J. Math. Phys. , vol.32 , pp. 924-927
    • Majid, S.1
  • 25
    • 36449004758 scopus 로고
    • C-statistical quantum groups and weyl algebras
    • S. Majid, "C-statistical quantum groups and Weyl algebras," J. Math. Phys. 33, 3431-3444 (1992).
    • (1992) J. Math. Phys. , vol.33 , pp. 3431-3444
    • Majid, S.1
  • 26
    • 0001756908 scopus 로고
    • Dual non-abelian duality and the drinfeld double
    • C. Klimcik and P. Severa, "Dual non-abelian duality and the Drinfeld double," Phys. Lett. B 351, 455-462 (1995).
    • (1995) Phys. Lett. B , vol.351 , pp. 455-462
    • Klimcik, C.1    Severa, P.2
  • 27
    • 0041196632 scopus 로고    scopus 로고
    • Poisson-lie T-duality for quasitriangular lie bialgebras
    • in press
    • E. Beggs and S. Majid, "Poisson-Lie T-duality for quasitriangular Lie bialgebras," Commun. Math. Phys. (2000) (in press).
    • (2000) Commun. Math. Phys.
    • Beggs, E.1    Majid, S.2
  • 28
    • 84973999031 scopus 로고
    • Matched pairs of lie groups associated to solutions of the Yang-Baxter equations
    • S. Majid, "Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations," Pac. J. Math. 141, 311-332 (1990).
    • (1990) Pac. J. Math. , vol.141 , pp. 311-332
    • Majid, S.1
  • 29
    • 0002808970 scopus 로고
    • Hopf-von neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations
    • S. Majid, "Hopf-von Neumann algebra bicrossproducts, Kac algebra bicrossproducts, and the classical Yang-Baxter equations," J. Funct. Anal. 95, 291-319 (1991).
    • (1991) J. Funct. Anal. , vol.95 , pp. 291-319
    • Majid, S.1
  • 30
    • 0032210257 scopus 로고    scopus 로고
    • Hopf algebras, cyclic cohomology and the transverse index theory
    • A. Connes and H. Moscovici, "Hopf algebras, cyclic cohomology and the transverse index theory," Commun. Math. Phys. 198, 199-246 (1998).
    • (1998) Commun. Math. Phys. , vol.198 , pp. 199-246
    • Connes, A.1    Moscovici, H.2
  • 31
    • 0032257297 scopus 로고    scopus 로고
    • Hopf algebras, renormalization and noncommutative geometry
    • A. Connes and D. Kreimer, "Hopf algebras, renormalization and noncommutative geometry," Commun. Math. Phys. 199, 203-242 (1998).
    • (1998) Commun. Math. Phys. , vol.199 , pp. 203-242
    • Connes, A.1    Kreimer, D.2
  • 33
    • 34249960869 scopus 로고
    • Ribbon graphs and their invariants derived from quantum groups
    • N. Yu. Reshetikhin and V. G. Turaev, "Ribbon graphs and their invariants derived from quantum groups," Commun. Math. Phys. 127(1), 1-26 (1990).
    • (1990) Commun. Math. Phys. , vol.127 , Issue.1 , pp. 1-26
    • Reshetikhin, N.Yu.1    Turaev, V.G.2
  • 34
    • 84968518084 scopus 로고
    • Polynomial invariants of knots via von neumann algebras
    • V. F. R. Jones, "Polynomial invariants of knots via von Neumann algebras," Bull. Am. Math. Soc. 12, 103-111 (1985).
    • (1985) Bull. Am. Math. Soc. , vol.12 , pp. 103-111
    • Jones, V.F.R.1
  • 37
    • 0007043606 scopus 로고    scopus 로고
    • Braided-lie bialgebras
    • S. Majid, "Braided-lie bialgebras," Pac. J. Math. 192, 329-356 (2000).
    • (2000) Pac. J. Math. , vol.192 , pp. 329-356
    • Majid, S.1
  • 39
    • 85007947259 scopus 로고
    • Twisted SU(2)-group, an example of a non-commutative differential calculus
    • S. L. Woronowicz, "Twisted SU(2)-group, an example of a non-commutative differential calculus," Publ. RIMS (Kyoto) 23, 117-181 (1987).
    • (1987) Publ. RIMS (Kyoto) , vol.23 , pp. 117-181
    • Woronowicz, S.L.1
  • 41
    • 0032209486 scopus 로고    scopus 로고
    • Quantum and braided diffeomorphism groups
    • S. Majid, "Quantum and braided diffeomorphism groups," J. Geom. Phys. 28, 94-128 (1998).
    • (1998) J. Geom. Phys. , vol.28 , pp. 94-128
    • Majid, S.1
  • 42
    • 0002785466 scopus 로고
    • Hamiltonian structures on lie groups, lie bialgebras and the geometric meaning of the classical Yang-Baxter equations
    • V. G. Drinfeld, "Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations," Sov. Math. Dokl. 27, 68 (1983).
    • (1983) Sov. Math. Dokl. , vol.27 , pp. 68
    • Drinfeld, V.G.1
  • 43
    • 4944264899 scopus 로고
    • Reduction of hamiltonian systems, affine lie algebras and lax equations II
    • A. G. Reyman and M. A. Semenov-Tian-Shansky, "Reduction of Hamiltonian systems, affine Lie algebras and Lax equations II," Invent. Math. 63, 423-432 (1981).
    • (1981) Invent. Math. , vol.63 , pp. 423-432
    • Reyman, A.G.1    Semenov-Tian-Shansky, M.A.2
  • 44
    • 0040877091 scopus 로고
    • On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)
    • A. Macfarlane, "On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)," J. Phys. A 22, 4581 (1989).
    • (1989) J. Phys. A , vol.22 , pp. 4581
    • Macfarlane, A.1
  • 45
    • 36149029891 scopus 로고
    • q(2) and the q-analogue of the boson operators
    • q(2) and the q-analogue of the boson operators," J. Phys. A 22, L873 (1989).
    • (1989) J. Phys. A , vol.22
    • Biedenharn, L.C.1
  • 46
    • 84974497034 scopus 로고
    • On q-functions and a certain difference operator
    • F. H. Jackson, "On q-functions and a certain difference operator," Trans. R. Soc. Edin. 46, 253-281 (1908).
    • (1908) Trans. R. Soc. Edin. , vol.46 , pp. 253-281
    • Jackson, F.H.1
  • 47
    • 21844516393 scopus 로고
    • Algebraic q-integration and fourier theory on quantum and braided spaces
    • A. Kempf and S. Majid, "Algebraic q-integration and Fourier theory on quantum and braided spaces," J. Math. Phys. 35, 6802-6837 (1994).
    • (1994) J. Math. Phys. , vol.35 , pp. 6802-6837
    • Kempf, A.1    Majid, S.2
  • 48
    • 36448999327 scopus 로고
    • Braided momentum in the q-Poincaré group
    • S. Majid, "Braided momentum in the q-Poincaré group," J. Math. Phys. 34, 2045-2058 (1993).
    • (1993) J. Math. Phys. , vol.34 , pp. 2045-2058
    • Majid, S.1
  • 49
    • 0346405348 scopus 로고
    • Braided groups
    • S. Majid, "Braided groups," J. Pure Appl. Algebra 86, 187-221 (1993).
    • (1993) J. Pure Appl. Algebra , vol.86 , pp. 187-221
    • Majid, S.1
  • 50
    • 0000709289 scopus 로고
    • Braided matrix structure of q-Minkowski space and q-Poincaré group
    • S. Majid and U. Meyer, "Braided matrix structure of q-Minkowski space and q-Poincaré group," Z. Phys. C 63, 357-362 (1994).
    • (1994) Z. Phys. C , vol.63 , pp. 357-362
    • Majid, S.1    Meyer, U.2
  • 51
    • 21344489762 scopus 로고
    • Free braided differential calculus, braided binomial theorem and the braided exponential map
    • S. Majid, "Free braided differential calculus, braided binomial theorem and the braided exponential map," J. Math. Phys. 34, 4843-4856 (1993).
    • (1993) J. Math. Phys. , vol.34 , pp. 4843-4856
    • Majid, S.1
  • 52
    • 21844501570 scopus 로고
    • Q-epsilon tensor for quantum and braided spaces
    • S. Majid, "q-epsilon tensor for quantum and braided spaces," J. Math. Phys. 36, 1991-2007 (1995).
    • (1995) J. Math. Phys. , vol.36 , pp. 1991-2007
    • Majid, S.1
  • 53
    • 21844511551 scopus 로고
    • *-structures on braided spaces
    • S. Majid, "*-structures on braided spaces," J. Geom. Phys. 36, 4436-4449 (1995).
    • (1995) J. Geom. Phys. , vol.36 , pp. 4436-4449
    • Majid, S.1
  • 54
    • 0031116810 scopus 로고    scopus 로고
    • Quasi-* structure on q-Poincaré algebras
    • S. Majid, "Quasi-* structure on q-Poincaré algebras," J. Math. Phys. 22, 14-58 (1997).
    • (1997) J. Math. Phys. , vol.22 , pp. 14-58
    • Majid, S.1
  • 55
    • 21844495625 scopus 로고
    • Q-Euclidean space and quantum wick rotation by twisting
    • S. Majid, "q-Euclidean space and quantum Wick rotation by twisting," J. Math. Phys. 35, 5025-5034 (1994).
    • (1994) J. Math. Phys. , vol.35 , pp. 5025-5034
    • Majid, S.1
  • 56
    • 0030361197 scopus 로고    scopus 로고
    • Braided geometry of the conformal algebra
    • S. Majid, "Braided geometry of the conformal algebra," J. Phys. Geom. 37, 6495-6509 (1996).
    • (1996) J. Phys. Geom. , vol.37 , pp. 6495-6509
    • Majid, S.1
  • 58
    • 0001542822 scopus 로고
    • Orthogonal polynomials in connection with quantum groups
    • edited by P. Neval, in NATO ASI Series C Kluwer, Dordrecht
    • T. H. Koornwinder, "Orthogonal polynomials in connection with quantum groups," in Orthogonal Polynomials: Theory and Practice, edited by P. Neval, no. 294 in NATO ASI Series C (Kluwer, Dordrecht 1990), pp. 257-292.
    • (1990) Orthogonal Polynomials: Theory and Practice , Issue.294 , pp. 257-292
    • Koornwinder, T.H.1
  • 59
    • 0030570697 scopus 로고    scopus 로고
    • Quantum deformation of quantum gravity
    • S. Major and L. Smolin, "Quantum deformation of quantum gravity," Nucl. Phys. B 473, 267-290 (1996).
    • (1996) Nucl. Phys. B , vol.473 , pp. 267-290
    • Major, S.1    Smolin, L.2
  • 60
    • 0000545097 scopus 로고
    • Quantum and braided lie algebras
    • S. Majid, "Quantum and braided Lie algebras," J. Geom. Phys. 13, 307-356 (1994).
    • (1994) J. Geom. Phys. , vol.13 , pp. 307-356
    • Majid, S.1
  • 61
    • 1542798257 scopus 로고
    • Differential calculus on compact matrix pseudogroups (quantum groups)
    • S. L. Woronowicz, "Differential calculus on compact matrix pseudogroups (quantum groups)," Commun. Math. Phys. 122, 125-170 (1989).
    • (1989) Commun. Math. Phys. , vol.122 , pp. 125-170
    • Woronowicz, S.L.1
  • 62
    • 0032043759 scopus 로고    scopus 로고
    • Classification of bicovariant differential calculi
    • S. Majid, "Classification of bicovariant differential calculi," J. Geom. Phys. 25, 119-140 (1998).
    • (1998) J. Geom. Phys. , vol.25 , pp. 119-140
    • Majid, S.1
  • 63
    • 0033423944 scopus 로고    scopus 로고
    • Quantum geometry of field extensions
    • S. Majid, "Quantum geometry of field extensions," J. Math. Phys. 40, 2311-2323 (1999).
    • (1999) J. Math. Phys. , vol.40 , pp. 2311-2323
    • Majid, S.1
  • 64
    • 0033567793 scopus 로고    scopus 로고
    • Quasitriangular and differential structures on bicrossproduct hopf algebras
    • E. Beggs and S. Majid, "Quasitriangular and differential structures on bicrossproduct Hopf algebras," J. Algebra 219, 682-727 (1999).
    • (1999) J. Algebra , vol.219 , pp. 682-727
    • Beggs, E.1    Majid, S.2
  • 65
    • 0032206103 scopus 로고    scopus 로고
    • Quantum differentials and the q-monopole revisited
    • T. Brzeziński and S. Majid, "Quantum differentials and the q-monopole revisited," Acta Appl. Math. 54, 185-232 (1998).
    • (1998) Acta Appl. Math. , vol.54 , pp. 185-232
    • Brzeziński, T.1    Majid, S.2
  • 66
    • 0347062767 scopus 로고
    • Quantum spheres
    • P. Podles, "Quantum spheres," Lett. Math. Phys. 14, 193-202 (1987).
    • (1987) Lett. Math. Phys. , vol.14 , pp. 193-202
    • Podles, P.1
  • 67
    • 25444450141 scopus 로고
    • Quantum group gauge theory on quantum spaces
    • Erratum. 167, 235 (1995)
    • T. Brzeziński and S. Majid, "Quantum group gauge theory on quantum spaces," Commun. Math. Phys. 157, 591-638 (1993); Erratum. 167, 235 (1995).
    • (1993) Commun. Math. Phys. , vol.157 , pp. 591-638
    • Brzeziński, T.1    Majid, S.2
  • 68
    • 0033201493 scopus 로고    scopus 로고
    • Projective module description of the q-monopole
    • P. Hajac and S. Majid, "Projective module description of the q-monopole," Commun. Math. Phys. 206, 246-464 (1999).
    • (1999) Commun. Math. Phys. , vol.206 , pp. 246-464
    • Hajac, P.1    Majid, S.2
  • 70
    • 85037765373 scopus 로고    scopus 로고
    • Quantum geometry of algebra factorisations and coalgebra bundles
    • T. Brzeziński and S. Majid, "Quantum geometry of algebra factorisations and coalgebra bundles," to appear in Commun. Math. Phys.
    • Commun. Math. Phys.
    • Brzeziński, T.1    Majid, S.2
  • 71
    • 0033130143 scopus 로고    scopus 로고
    • Quantum and braided group Riemannian geometry
    • S. Majid, "Quantum and braided group Riemannian geometry," J. Geom. Phys. 30, 113-146 (1999).
    • (1999) J. Geom. Phys. , vol.30 , pp. 113-146
    • Majid, S.1
  • 72
    • 0000277570 scopus 로고
    • Representations, duals and quantum doubles of monoidal categories
    • Ser. II
    • S. Majid, "Representations, duals and quantum doubles of monoidal categories," Suppl. Rend. Circ. Mat. Palermo, Ser. II 26, 197-206 (1991).
    • (1991) Suppl. Rend. Circ. Mat. Palermo , vol.26 , pp. 197-206
    • Majid, S.1
  • 73
    • 0039417122 scopus 로고
    • Some physical applications of category theory
    • S. Majid, "Some physical applications of category theory," Lect. Notes Phys. 375, 131-142 (1991).
    • (1991) Lect. Notes Phys. , vol.375 , pp. 131-142
    • Majid, S.1


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