Groupoids and compact quantum groups

Albert Sheu

Banach Center Publications (1997)

  • Volume: 40, Issue: 1, page 41-50
  • ISSN: 0137-6934

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Sheu, Albert. "Groupoids and compact quantum groups." Banach Center Publications 40.1 (1997): 41-50. <http://eudml.org/doc/252206>.

@article{Sheu1997,
author = {Sheu, Albert},
journal = {Banach Center Publications},
keywords = {groupoid -algebras; compact quantum groups groupoids; groupoids},
language = {eng},
number = {1},
pages = {41-50},
title = {Groupoids and compact quantum groups},
url = {http://eudml.org/doc/252206},
volume = {40},
year = {1997},
}

TY - JOUR
AU - Sheu, Albert
TI - Groupoids and compact quantum groups
JO - Banach Center Publications
PY - 1997
VL - 40
IS - 1
SP - 41
EP - 50
LA - eng
KW - groupoid -algebras; compact quantum groups groupoids; groupoids
UR - http://eudml.org/doc/252206
ER -

References

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  1. [B-D] A. Belavin and V. Drinfeld, Solutions of the classical Yang-Baxter equation for simple Lie algebras, Func. Anal. Appl. 16 (1982). 
  2. [Co] A. Connes, A survey of foliation and operator algebras, Proc. Symp. Pure Math. Vol. 38, Part I, AMS, Providence, 1982, 521-628. 
  3. [CuM] R. E. Curto and P. S. Muhly, C*-algebras of multiplication operators on Bergman spaces, J. Func. Anal. 64 (1985), 315-329. Zbl0583.46049
  4. [D] V. G. Drinfeld, Quantum groups, Proc. I.C.M. Berkeley 1986, Vol. 1, 789-820, Amer. Math. Soc., Providence, 1987. 
  5. [H] H. Hiller, Geometry of Coxeter Groups, Research Notes in Math. Vol. 54, Pitman, Boston, 1982. Zbl0483.57002
  6. [La] C. Lance, An explicit description of the fundamental unitary for S U ( 2 ) q , Comm. Math. Phys. 164 (1994), 1-15. Zbl0818.17014
  7. [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. 
  8. [LuWe] J. H. Lu and A. Weinstein, Poisson Lie groups, dressing transformations and Bruhat decompositions, J. Diff. Geom. 31 (1990), 501-526. Zbl0673.58018
  9. [MRe] P. S. Muhly and J. N. Renault, C*-algebras of multivariable Wiener-Hopf operators, Trans. Amer. Math. Soc. 274 (1982), 1-44. Zbl0509.46049
  10. [N] G. Nagy, On the Haar measure of the quantum SU(N) group, Comm. Math. Phys. 153 (1993), 217-228. Zbl0779.17015
  11. [Po] P. Podleś, Quantum spheres, Letters Math. Phys. 14 (1987), 193-202. Zbl0634.46054
  12. [Re] J. Renault, A Groupoid Approach to C*-algebras, Lecture Notes in Mathematics, Vol. 793, Springer-Verlag, New York, 1980. Zbl0433.46049
  13. [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. Zbl0715.17015
  14. [Ri1] M. A. Rieffel, Deformation quantization and operator algebras, in 'Proc. Symp.Pure Math., Vol. 51', AMS, Providence, 1990, pp. 411-423. 
  15. [Ri2] M. A. Rieffel, Deformation quantization for actions of d , Memoirs of AMS, Vol. 106, No. 506, 1993. 
  16. [Ri3] M. A. Rieffel, Compact quantum groups associated with toral subgroups, in 'Contemporary Mathematics', Vol. 145, AMS, Providence, 1993, pp. 465-491. Zbl0795.17017
  17. [Ri4] M. A. Rieffel, Non-compact quantum groups associated with abelian subgroups, Comm. Math. Phys., 171 (1995), 181-201. Zbl0857.17014
  18. [Sh1] A. J. L. Sheu, Reinhardt domains, boundary geometry and Toeplitz C*-algebras, Journal of Functional Analysis, 92 (1990), 264-311. 
  19. [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. Zbl0719.58042
  20. [Sh3] A. J. L. Sheu, Leaf-preserving quantizations of Poisson SU(2) are not coalgebra homomorphisms, Comm. Math. Phys., 172 (1995), 287-292. Zbl0839.46073
  21. [Sh4] A. J. L. Sheu, Symplectic leaves and deformation quantization, Proc. Amer. Math. Soc., 124 (1996), 95-100. Zbl0846.46046
  22. [Sh5] A. J. L. Sheu, Compact quantum groups and groupoid C*-algebras, to appear in J. Func. Anal. 
  23. [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.) 
  24. [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. 
  25. [VSo1] L. L. Vaksman and Ya. S. Soibelman, Algebra of functions on the quantum group SU(2), Func. Anal. Appl. 22 (1988), 170-181. 
  26. [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. 
  27. [Wa] S. Wang, Classification of quantum groups S U q ( n ) , preprint. 
  28. [We] A. Weinstein, The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), 523-557. Zbl0524.58011
  29. [Wo1] S. L. Woronowicz, Twisted SU(2) group: an example of a non-commutative differential calculus, Publ. RIMS. 23 (1987), 117-181. 
  30. [Wo2] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665. Zbl0627.58034
  31. [Wo3] S. L. Woronowicz, Tannaka-Krein duality for compact matrix pseudogroups, twisted SU(N) groups, Invent. Math. 93 (1988), 35-76. Zbl0664.58044
  32. [Wo4] S. L. Woronowicz, Quantum SU(2) and E(2) groups. Contraction procedure, Comm. Math. Phys. 149 (1992), 637-652. Zbl0759.17009

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