메뉴 건너뛰기




Volumn 22, Issue 1, 1997, Pages 14-58

Quasi-* structure on q-Poincaré algebras

Author keywords

Braided groups; Hopf algebras; q Poincar quantum groups

Indexed keywords


EID: 0031116810     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(96)00022-8     Document Type: Article
Times cited : (18)

References (63)
  • 1
    • 0000481618 scopus 로고
    • Quantum groups
    • ed. A. Gleason American Mathematical Society, Providence, RI
    • [1] V.G. Drinfeld, Quantum groups, in: Proc. ICM, ed. A. Gleason (American Mathematical Society, Providence, RI, 1987) pp.798-820.
    • (1987) Proc. ICM , pp. 798-820
    • Drinfeld, V.G.1
  • 2
    • 0040323775 scopus 로고
    • A q-difference analog of U(g) and the Yang-Baxter equation
    • [2] M. Jimbo, A q-difference analog of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985) 63-69.
    • (1985) Lett. Math. Phys. , vol.10 , pp. 63-69
    • Jimbo, M.1
  • 3
    • 84908807046 scopus 로고
    • Examples of braided groups and braided matrices
    • [3] S. Majid, Examples of braided groups and braided matrices, J. Math. Phys. 32 (1991) 3246-3253.
    • (1991) J. Math. Phys. , vol.32 , pp. 3246-3253
    • Majid, S.1
  • 4
    • 0000124925 scopus 로고
    • On q-regularization
    • [4] S. Majid, On q-regularization, Int. J. Mod. Phys. A 5 (1990) 4689-4696.
    • (1990) Int. J. Mod. Phys. A , vol.5 , pp. 4689-4696
    • Majid, S.1
  • 5
    • 36149030193 scopus 로고
    • Hopf algebras for physics at the Planck scale
    • [5] S. Majid, Hopf algebras for physics at the Planck scale, J. Classical and Quantum Gravity 5 (1988) 1587-1606.
    • (1988) J. Classical and Quantum Gravity , vol.5 , pp. 1587-1606
    • Majid, S.1
  • 8
    • 21844511551 scopus 로고
    • *-Structures on braided spaces
    • August 1994
    • [8] S. Majid, *-Structures on braided spaces, August 1994, J. Math. Phys. 36 (1995) 4436-4449.
    • (1995) J. Math. Phys. , vol.36 , pp. 4436-4449
    • Majid, S.1
  • 9
    • 36448999327 scopus 로고
    • Braided momentum in the q-Poincaré group
    • [9] S. Majid, Braided momentum in the q-Poincaré group, J. Math. Phys. 34 (1993) 2045-2058.
    • (1993) J. Math. Phys. , vol.34 , pp. 2045-2058
    • Majid, S.1
  • 10
    • 1542483491 scopus 로고
    • Compact matrix pseudo groups
    • [10] S.L. Woronowicz, Compact matrix pseudo groups, Commun. Math. Phys. 111 (1987) 613-665.
    • (1987) Commun. Math. Phys. , vol.111 , pp. 613-665
    • Woronowicz, S.L.1
  • 11
    • 0041587326 scopus 로고
    • Some remarks on the q-Poincaré algebra in R-matrix form
    • eds. H.-D. Doebner, V.K. Dobrev and P. Nattermann World Scientific, Singapore
    • [11] S. Majid, Some remarks on the q-Poincaré algebra in R-matrix form, in: Nonlinear, Deformed and Irreversible Quantum Systems, eds. H.-D. Doebner, V.K. Dobrev and P. Nattermann (World Scientific, Singapore, 1995) pp.352-384.
    • (1995) Nonlinear, Deformed and Irreversible Quantum Systems , pp. 352-384
    • Majid, S.1
  • 13
    • 0001940379 scopus 로고
    • Quasitriangular Hopf algebras and Yang-Baxter equations
    • [13] S. Majid, Quasitriangular Hopf algebras and Yang-Baxter equations, Int. J. Modern Phys. A 5 (1) (1990) 1-91.
    • (1990) Int. J. Modern Phys. A , vol.5 , Issue.1 , pp. 1-91
    • Majid, S.1
  • 15
    • 0002359613 scopus 로고
    • Cross products by braided groups and bosonization
    • [15] S. Majid, Cross products by braided groups and bosonization, J. Algebra 163 (1994) 165-190.
    • (1994) J. Algebra , vol.163 , pp. 165-190
    • Majid, S.1
  • 16
    • 0000805003 scopus 로고
    • QuasiHopf algebras
    • [16] V.G. Drinfeld, QuasiHopf algebras, Leningrad Math. J. 1 (1990) 1419-1457.
    • (1990) Leningrad Math. J. , vol.1 , pp. 1419-1457
    • Drinfeld, V.G.1
  • 17
    • 0002293135 scopus 로고
    • Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices)
    • eds. M.-L. Ge and H.J. de Vega World Scientific, Singapore
    • [17] S. Majid, Beyond supersymmetry and quantum symmetry (an introduction to braided groups and braided matrices), in; Quantum Groups Integrable Statistical Models and Knot Theory, eds. 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
  • 18
    • 85170172687 scopus 로고
    • Algebras and Hopf algebras in braided categories
    • Marcel Dekker, New York
    • [18] S. Majid, Algebras and Hopf algebras in braided categories, Lecture Notes in Pure and Applied Mathematics, Vol. 158 (Marcel Dekker, New York, 1994) pp.55-105.
    • (1994) Lecture Notes in Pure and Applied Mathematics , vol.158 , pp. 55-105
    • Majid, S.1
  • 19
    • 0040654365 scopus 로고    scopus 로고
    • Introduction to braided geometry and q-Minkowski space
    • eds. L. Castellani and J. Wess IOS Press, Amsterdam
    • [19] S. Majid, Introduction to braided geometry and q-Minkowski space, in: Proc. International School of Physics 'Enrico Fermi' CXXVII, eds. L. Castellani and J. Wess (IOS Press, Amsterdam, 1996).
    • (1996) Proc. International School of Physics 'Enrico Fermi' CXXVII
    • Majid, S.1
  • 20
    • 22244487904 scopus 로고
    • Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group
    • [20] S. Majid, Braided matrix structure of the Sklyanin algebra and of the quantum Lorentz group, Commun. Math. Phys. 156 (1993) 607-638.
    • (1993) Commun. Math. Phys. , vol.156 , pp. 607-638
    • Majid, S.1
  • 21
    • 21144470191 scopus 로고
    • Quantum and braided linear algebra
    • [21] S. Majid, Quantum and braided linear algebra, J. Math. Phys. 34 (1993) 1176-1196.
    • (1993) J. Math. Phys. , vol.34 , pp. 1176-1196
    • Majid, S.1
  • 22
    • 21344489762 scopus 로고
    • Free braided differential calculus, braided binomial theorem and the braided exponential map
    • [22] S. Majid, Free braided differential calculus, braided binomial theorem and the braided exponential map, J. Math. Phys. 34 (1993) 4843-4856.
    • (1993) J. Math. Phys. , vol.34 , pp. 4843-4856
    • Majid, S.1
  • 23
    • 21844501570 scopus 로고
    • q-epsilon tensor for quantum and braided spaces
    • [23] S. Majid, q-epsilon tensor for quantum and braided spaces, J. Math. Phys. 36 (1995) 1991-2007.
    • (1995) J. Math. Phys. , vol.36 , pp. 1991-2007
    • Majid, S.1
  • 24
    • 21844516393 scopus 로고
    • Algebraic q-integration and Fourier theory on quantum and braided spaces
    • [24] A. Kempf and S. Majid, Algebraic q-integration and Fourier theory on quantum and braided spaces, J. Math. Phys. 35 (1994) 6802-6837.
    • (1994) J. Math. Phys. , vol.35 , pp. 6802-6837
    • Kempf, A.1    Majid, S.2
  • 25
    • 0000363727 scopus 로고
    • The quantum double as quantum mechanics
    • [25] S. Majid, The quantum double as quantum mechanics, J. Geom. Phys. 13 (1994) 169-202.
    • (1994) J. Geom. Phys. , vol.13 , pp. 169-202
    • Majid, S.1
  • 26
    • 21844500407 scopus 로고
    • q-Lorentz group and braided coaddition on q-Minkoswki space
    • [26] U. Meyer, q-Lorentz group and braided coaddition on q-Minkoswki space, Commun. Math. Phys. 168 (1995) 249-264.
    • (1995) Commun. Math. Phys. , vol.168 , pp. 249-264
    • Meyer, U.1
  • 27
    • 0000709289 scopus 로고
    • Braided matrix structure of q-Minkowski space and q-Poincaré group
    • [27] S. Majid and U. Meyer, Braided matrix structure of q-Minkowski space and q-Poincaré group, Z. Phys. C 63 (1994) 357-362.
    • (1994) Z. Phys. C , vol.63 , pp. 357-362
    • Majid, S.1    Meyer, U.2
  • 28
    • 21844495625 scopus 로고
    • q-Euclidean space and quantum Wick rotation by twisting
    • [28] S. Majid, q-Euclidean space and quantum Wick rotation by twisting, J. Math. Phys. 35 (1994) 5025-5034.
    • (1994) J. Math. Phys. , vol.35 , pp. 5025-5034
    • Majid, S.1
  • 33
    • 0000843573 scopus 로고
    • Reality in the differential calculus on q-Euclidean spaces
    • [33] O. Ogievetsky and B. Zumino, Reality in the differential calculus on q-Euclidean spaces, Lett. Math. Phys. 25 (1992) 121-130.
    • (1992) Lett. Math. Phys. , vol.25 , pp. 121-130
    • Ogievetsky, O.1    Zumino, B.2
  • 35
    • 0002127258 scopus 로고
    • Rank of quantum groups and braided groups in dual form
    • Springer, Berlin
    • [35] S. Majid, Rank of quantum groups and braided groups in dual form, Lecture Notes in Mathematics, Vol. 1510 (Springer, Berlin, 1992) pp.79-89.
    • (1992) Lecture Notes in Mathematics , vol.1510 , pp. 79-89
    • Majid, S.1
  • 36
    • 0346405348 scopus 로고
    • Braided groups
    • [36] S. Majid, Braided groups, J. Pure Appl. Algebra 86 (1993) 187-221.
    • (1993) J. Pure Appl. Algebra , vol.86 , pp. 187-221
    • Majid, S.1
  • 37
    • 34249960869 scopus 로고
    • Ribbon graphs and their invariants derived from quantum groups
    • [37] N.Yu. Reshetikhin and V.G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Commun. Math. Phys. 127 (1) (1990) 1-26.
    • (1990) Commun. Math. Phys. , vol.127 , Issue.1 , pp. 1-26
    • Reshetikhin, N.Yu.1    Turaev, V.G.2
  • 38
    • 0000805004 scopus 로고
    • On almost-cocommutative Hopf algebras
    • [38] V.G. Drinfeld, On almost-cocommutative Hopf algebras, Leningrad Math. J. 1 (1990) 341-342.
    • (1990) Leningrad Math. J. , vol.1 , pp. 341-342
    • Drinfeld, V.G.1
  • 39
    • 0001056033 scopus 로고
    • Braided groups and algebraic quantum field theories
    • [39] S. Majid, Braided groups and algebraic quantum field theories, Lett. Math. Phys. 22 (1991) 167-176.
    • (1991) Lett. Math. Phys. , vol.22 , pp. 167-176
    • Majid, S.1
  • 40
    • 0002030963 scopus 로고
    • Cross product quantization, nonabelian cohomology and twisting of Hopf algebras
    • eds. V.K. Dobrev, H.-D. Doebner and A.G. Ushveridze World Scientific, Singapore
    • [40] S. Majid, Cross product quantization, nonabelian cohomology and twisting of Hopf algebras, in: Generalised Symmetries in Physics, eds. V.K. Dobrev, H.-D. Doebner and A.G. Ushveridze (World Scientific, Singapore, 1994) pp.13-41.
    • (1994) Generalised Symmetries in Physics , pp. 13-41
    • Majid, S.1
  • 41
    • 84972558524 scopus 로고
    • Braided group of Hopf algebras obtained by twisting
    • [41] D.I. Gurevich and S. Majid, Braided group of Hopf algebras obtained by twisting, Pac. J. Math. 162 (1994) 27-44.
    • (1994) Pac. J. Math. , vol.162 , pp. 27-44
    • Gurevich, D.I.1    Majid, S.2
  • 42
    • 0002470078 scopus 로고
    • Quantum group structure in a fermionic extension of the quantum harmonic oscillator
    • [42] A. Macfarlane and S. Majid, Quantum group structure in a fermionic extension of the quantum harmonic oscillator, Phys. Lett. B 268 (1991) 71-74.
    • (1991) Phys. Lett. B , vol.268 , pp. 71-74
    • Macfarlane, A.1    Majid, S.2
  • 43
    • 21844484406 scopus 로고
    • Non-standard quantum group and superization
    • [43] S. Majid and M.J. Rodriguez-Plaza, Non-standard quantum group and superization, J. Math. Phys. 36 (1995) 7071-7097.
    • (1995) J. Math. Phys. , vol.36 , pp. 7071-7097
    • Majid, S.1    Rodriguez-Plaza, M.J.2
  • 46
    • 0002101120 scopus 로고
    • Transmutation theory and rank for quantum braided groups
    • [46] S. Majid, Transmutation theory and rank for quantum braided groups, Math. Proc. Camb. Phil. Soc. 113 (1993) 45-70.
    • (1993) Math. Proc. Camb. Phil. Soc. , vol.113 , pp. 45-70
    • Majid, S.1
  • 47
    • 46549103268 scopus 로고
    • The structure of Hopf algebras with a projection
    • [47] D. Radford, The structure of Hopf algebras with a projection, J. Algebra 92 (1985) 322-347.
    • (1985) J. Algebra , vol.92 , pp. 322-347
    • Radford, D.1
  • 48
    • 0010998549 scopus 로고
    • Quantum group duality in vertex models and other results in the theory of quasitriangular Hopf algebras
    • eds. L.-L. Chau and W. Nahm, Tahoe (1989), Nato-ASI Series B, Plenum Press, New York
    • [48] S. Majid, Quantum group duality in vertex models and other results in the theory of quasitriangular Hopf algebras, in: Proc. XVIIIth DGM, eds. L.-L. Chau and W. Nahm, Tahoe (1989), Nato-ASI Series B, Vol. 245 (Plenum Press, New York, 1989) pp.373-386.
    • (1989) Proc. XVIIIth DGM , vol.245 , pp. 373-386
    • Majid, S.1
  • 50
    • 21344491613 scopus 로고
    • On the addtion of quantum matrices
    • [50] S. Majid, On the addtion of quantum matrices, J. Math. Phys. 35 (1994) 2617-2633.
    • (1994) J. Math. Phys. , vol.35 , pp. 2617-2633
    • Majid, S.1
  • 51
    • 85012553668 scopus 로고    scopus 로고
    • Glueing operation for R-matrices, quantum groups and link invariants of Hecke type
    • [51] S. Majid and M. Markl, Glueing operation for R-matrices, quantum groups and link invariants of Hecke type, Math. Proc. Camb. Phil. Soc. 119 (1996).
    • (1996) Math. Proc. Camb. Phil. Soc. , vol.119
    • Majid, S.1    Markl, M.2
  • 53
    • 51249175198 scopus 로고
    • Quantum deformation of Lorentz group
    • [53] P. Podles and S.L. Woronowicz, Quantum deformation of Lorentz group, Commun. Math. Phys. 130 (1990) 381-431.
    • (1990) Commun. Math. Phys. , vol.130 , pp. 381-431
    • Podles, P.1    Woronowicz, S.L.2
  • 54
    • 0000545097 scopus 로고
    • Quantum and braided Lie algebras
    • [54] S. Majid, Quantum and braided Lie algebras, J. Geom. Phys. 13 (1994) 307-356.
    • (1994) J. Geom. Phys. , vol.13 , pp. 307-356
    • Majid, S.1
  • 58
  • 59
    • 0001776061 scopus 로고
    • Quantum group-symmetric Fock-spaces and Bargmann-Fock representation
    • [59] A. Kempf, Quantum group-symmetric Fock-spaces and Bargmann-Fock representation, Lett. Math. Phys. 26 (1992) 1-12.
    • (1992) Lett. Math. Phys. , vol.26 , pp. 1-12
    • Kempf, A.1
  • 60
    • 44949285483 scopus 로고
    • Covariant differential calculus on the quantum hyperplane
    • [60] J. Wess and B. Zumino, Covariant differential calculus on the quantum hyperplane, Proc. Suppl. Nucl. Phys. B 18 (1990) 302.
    • (1990) Proc. Suppl. Nucl. Phys. B , vol.18 , pp. 302
    • Wess, J.1    Zumino, B.2
  • 61
    • 0001436895 scopus 로고
    • A q-deformed quantum mechanical toy model
    • [61] J. Schwenk and J. Wess, A q-deformed quantum mechanical toy model, Phys. Lett. B. 291 (1992) 273-277.
    • (1992) Phys. Lett. B. , vol.291 , pp. 273-277
    • Schwenk, J.1    Wess, J.2
  • 62
    • 0000977747 scopus 로고
    • Braided groups and quantum Fourier transform
    • [62] V.V. Lyubashenko and S. Majid, Braided groups and quantum Fourier transform, J. Algebra 166 (1994) 506-528.
    • (1994) J. Algebra , vol.166 , pp. 506-528
    • Lyubashenko, V.V.1    Majid, S.2
  • 63
    • 0000332783 scopus 로고
    • q and its Hilbert space structure
    • q and its Hilbert space structure, Int. J. Mod. Phys. A 26 (1993) 4679-4729.
    • (1993) Int. J. Mod. Phys. A , vol.26 , pp. 4679-4729
    • Fiore, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.