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1997 | 40 | 1 | 41-50
Tytuł artykułu

Groupoids and compact quantum groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
41-50
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA
Bibliografia
  • [B-D] A. Belavin and V. Drinfeld, Solutions of the classical Yang-Baxter equation for simple Lie algebras, Func. Anal. Appl. 16 (1982).
  • [Co] A. Connes, A survey of foliation and operator algebras, Proc. Symp. Pure Math. Vol. 38, Part I, AMS, Providence, 1982, 521-628.
  • [CuM] R. E. Curto and P. S. Muhly, C*-algebras of multiplication operators on Bergman spaces, J. Func. Anal. 64 (1985), 315-329.
  • [D] V. G. Drinfeld, Quantum groups, Proc. I.C.M. Berkeley 1986, Vol. 1, 789-820, Amer. Math. Soc., Providence, 1987.
  • [H] H. Hiller, Geometry of Coxeter Groups, Research Notes in Math. Vol. 54, Pitman, Boston, 1982.
  • [La] C. Lance, An explicit description of the fundamental unitary for $SU(2)_q$, Comm. Math. Phys. 164 (1994), 1-15.
  • [LeSo] S. Levendorskii and Ya. Soibelman, Algebras of functions on compact quantum groups, Schubert cells and quantum tori, Comm. Math. Phys., 139 (1991), 141-170.
  • [LuWe] J. H. Lu and A. Weinstein, Poisson Lie groups, dressing transformations and Bruhat decompositions, J. Diff. Geom. 31 (1990), 501-526.
  • [MRe] P. S. Muhly and J. N. Renault, C*-algebras of multivariable Wiener-Hopf operators, Trans. Amer. Math. Soc. 274 (1982), 1-44.
  • [N] G. Nagy, On the Haar measure of the quantum SU(N) group, Comm. Math. Phys. 153 (1993), 217-228.
  • [Po] P. Podleś, Quantum spheres, Letters Math. Phys. 14 (1987), 193-202.
  • [Re] J. Renault, A Groupoid Approach to C*-algebras, Lecture Notes in Mathematics, Vol. 793, Springer-Verlag, New York, 1980.
  • [RTF] N. Yu. Reshetikhin, L. A. Takhtadzhyan, and L. D. Faddeev, Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1 (1990), 193-225.
  • [Ri1] M. A. Rieffel, Deformation quantization and operator algebras, in 'Proc. Symp.Pure Math., Vol. 51', AMS, Providence, 1990, pp. 411-423.
  • [Ri2] M. A. Rieffel, Deformation quantization for actions of $ℝ^d$, Memoirs of AMS, Vol. 106, No. 506, 1993.
  • [Ri3] M. A. Rieffel, Compact quantum groups associated with toral subgroups, in 'Contemporary Mathematics', Vol. 145, AMS, Providence, 1993, pp. 465-491.
  • [Ri4] M. A. Rieffel, Non-compact quantum groups associated with abelian subgroups, Comm. Math. Phys., 171 (1995), 181-201.
  • [Sh1] A. J. L. Sheu, Reinhardt domains, boundary geometry and Toeplitz C*-algebras, Journal of Functional Analysis, 92 (1990), 264-311.
  • [Sh2] A. J. L. Sheu, Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere, Comm. Math. Phys. 135 (1991), 217-232.
  • [Sh3] A. J. L. Sheu, Leaf-preserving quantizations of Poisson SU(2) are not coalgebra homomorphisms, Comm. Math. Phys., 172 (1995), 287-292.
  • [Sh4] A. J. L. Sheu, Symplectic leaves and deformation quantization, Proc. Amer. Math. Soc., 124 (1996), 95-100.
  • [Sh5] A. J. L. Sheu, Compact quantum groups and groupoid C*-algebras, to appear in J. Func. Anal.
  • [So1] Ya. S. Soibelman, The algebra of functions on a compact quantum group, and its representations, Algebra Analiz. 2 (1990), 190-221. (Leningrad Math. J., 2 (1991), 161-178.)
  • [So2] Ya. S. Soibelman, Irreducible representations of the function algebra on the quantum group SU(n), and Schubert cells% , Soviet Math. Dokl. 40 (1990), 34-38.
  • [VSo1] L. L. Vaksman and Ya. S. Soibelman, Algebra of functions on the quantum group SU(2), Func. Anal. Appl. 22 (1988), 170-181.
  • [VSo2] L. L. Vaksman and Ya. S. Soibelman, The algebra of functions on the quantum group SU(n+1), and odd-dimensional quantum spheres, Leningrad Math. J. 2 (1991), 1023-1042.
  • [Wa] S. Wang, Classification of quantum groups $SU_q(n)$, preprint.
  • [We] A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), 523-557.
  • [Wo1] S. L. Woronowicz, Twisted SU(2) group: an example of a non-commutative differential calculus, Publ. RIMS. 23 (1987), 117-181.
  • [Wo2] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665.
  • [Wo3] S. L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups, twisted SU(N) groups, Invent. Math. 93 (1988), 35-76.
  • [Wo4] S. L. Woronowicz, Quantum SU(2) and E(2) groups. Contraction procedure, Comm. Math. Phys. 149 (1992), 637-652.
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Bibliografia
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