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An example of amenable Kac systems


Author: Chi-Keung Ng
Journal: Proc. Amer. Math. Soc. 130 (2002), 2995-2998
MSC (2000): Primary 46L05, 46L55; Secondary 43A07, 22D25
DOI: https://doi.org/10.1090/S0002-9939-02-06482-1
Published electronically: March 29, 2002
MathSciNet review: 1908922
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Abstract: By giving an interesting characterisation of amenable multiplicative unitaries, we show, in a very simple way, that bicrossproducts of amenable locally compact groups are both amenable and coamenable.


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  • 1. S. Baaj, Représentation régulière du groupe quantique des déplacements de Woronowicz, Astérisque (1995), no. 232, 11-48. MR 97a:46107
  • 2. S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de $C^{*}$-algèbres, Ann. scient. Éc. Norm. Sup., $4^{e}$ série, t. 26 (1993), 425-488. MR 94e:46127
  • 3. S. Baaj and G. Skandalis, Transformations pentagonales, C. R. Acad. Sci. Paris Ser. I Math. 327 (1998), no. 7, 623-628. MR 99k:28018
  • 4. E. Bédos, G.J. Murphy and L. Tuset, Co-Amenability of Compact Quantum Groups, J. Geom. Phys. 40 (2001), 130-153. CMP 2002:03
  • 5. M.E.B. Bekka, Amenable unitary reperesentations of locally compact groups, Invent. Math. 100 (1990), 383-401. MR 91g:22007
  • 6. M. Enock and J.-M. Schwartz, Algebres de Kac moyennables, Pacific J. Math. 125 (1986), 363-379. MR 88f:46126
  • 7. S. Majid, Hopf von Neumann algebra bicrossproducts, Kac algebra bicrossproducts and the classical Yang-Baxter equations, J. Funct. Anal. 95 (1991), 291-319. MR 92b:46088
  • 8. C.K. Ng, Morphisms of Multiplicative unitaries, J. Oper. Theory 38 (1997), 203-224. MR 99i:46044
  • 9. C.K. Ng, Amenability of Hopf $C^*$-algebras, Proceedings of the 17th OT conference (2000), 269-284. MR 2001g:46129
  • 10. C.K. Ng, Duality of Hopf $C^*$-algebras, preprint.
  • 11. C.K. Ng, Amenable representations and Reiter's property for Kac algebras, preprint.
  • 12. T. Yamanouchi, Bicrossproduct Kac algebras, Bicrossproduct groups and von Neumann algebras of Takesaki's type, Math. Scand. 71 (1992), 252-260. MR 94f:46097
  • 13. S. L. Woronowicz, From multiplicative unitaries to quantum groups, Internat. J. Math. 7 (1996), no.1, 127-149. MR 96k:46136

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Additional Information

Chi-Keung Ng
Affiliation: Department of Pure Mathematics, The Queen’s University of Belfast, Belfast BT7 1NN, United Kingdom
Email: c.k.ng@qub.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-02-06482-1
Received by editor(s): January 3, 2001
Received by editor(s) in revised form: May 9, 2001
Published electronically: March 29, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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