Amenability and co-amenability for locally compact quantum groups

International Journal of Mathematics

Volumn 14, Issue 8, 2003, Pages 865-884

  Bedos E ^a   Tuset, L ^b  

^a UNIVERSITY OF OSLO   (Norway)

^b OSLO METROPOLITAN UNIVERSITY   (Norway)

Author keywords

Amenability; Quantum groups; Representations and corepresentations

Indexed keywords

EID: 0344064053     PISSN: 0129167X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129167X03002046     Document Type: Article

References (27)

1. S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres, Ann. Sci. EC. Norm. Sup. 28 (1993), 425-488.
2. T. Banica, Representations of compact quantum groups and subfactors, J. Reine Angew. Math. 509 (1999), 167-198.
3. T. Banica, Fusion rules for representations of compact quantum groups, Expo. Math. 17 (1999), 313-338.
4. E. Bédos, G. J. Murphy and L. Tuset, Co-amenability of compact quantum groups, J. Geom. Phys. 40 (2001), 130-153.
5. E. Bédos, G. J. Murphy and L. Tuset, Amenability and co-amenability for algebraic quantum groups, Int. J. Math. Math. Sciences 31 (2002), 577-601.
6. E. Bédos, G. J. Murphy and L. Tuset, Amenability and co-amenability for algebraic quantum groups II, to appear in J. Fund. Anal. (2003).
7. E. Bédos, R. Conti and L. Tuset, On amenability and co-amenability for algebraic quantum groups and their representations, to appear in Can. J. Math. (2004).
8. M. E. B. Bekka, Amenable unitary representation of locally compact groups, Invent. Math. 100 (1990), 383-401.
9. E. Blanchard, Déformations de C*-algèbres de Hopf, Bull. Soc. Math. France 124 (1996), 141-215.
10. P. Desmedt, J. Quaegebeur and S. Vaes, Amenability and the bicrossed product construction, preprint, 2001.
11. J. Dixmier, Les C*-Algèbres et Leurs Représentations, Gauthiers-Villars, Paris, 1969.
12. M. Enock and J. M. Schwarte, Algebres de Kac moyennables, Pac. J. Math. 125 (1986), 363-379.
13. J. Kustermans, Locally compact quantum groups in the universal setting, Int. J. Math. 12 (2001), 289-338.
14. J. Kustermans and S. Vaes, Locally compact quantum groups, Ann. Scient. École Norm. Sup. 33 (2000), 837-934.
15. J. Kustermans and S. Vaes, Locally compact quantum groups in the von Neumann algebraic setting, Math. Scand. 92 (2003), 68-92.
16. R. Longo and J. E. Roberts, A theory of dimensions, K-Theory 11 (1997), 103-159.
17. C.-K. Ng, Amenability of Hopf C*-algebras, Proc. 17th OT Conf. (2000), pp. 269-284.
18. C.-K. Ng, Examples of amenable Kac algebras, Proc. Amer. Math. Soc. 130 (2002), 2995-2998.
19. A. L. Paterson, Amenability, Math. Surv. Monogr. 29, Amer. Math. Soc., Providence RI, 1988.
20. J. E. Roberts and L. Tuset, On the equality of q-dimension and intrinsic dimension, J. Pure Appl. Algebra 156 (2001), 329-343.
21. Z.-J. Ruan, Amenability of Hopf von Neumann algebras and Kac Algebras, J. Funct. Anal. 139 (1996), 466-499.
22. J. Tomiyama, Tensor products and projections of norm one in von Neumann algebras, Lecture Notes, University of Copenhagen, 1970.
23. S. Vaes, Examples of locally compact quantum groups through the bicrossed product construction, XIIIth Int. Con. Math. Phys., International Press, Boston, MA, 341-348, 2001.
24. S. Vaes and L. Vainerman, Extensions of locally compact quantum groups and the bicrossed product construction, preprint, 2001.
25. A. Van Daele, An algebraic framework for group duality, Adv. Math. 140 (1998), 323-366.
26. A. Van Daele, Multiplier Hopf algebras, Trans. Amer. Math. Soc. 342 (1994), 917-932.
27. D. Voiculescu, Amenability and Katz algebras, in Algèbres d'Opérateurs et leurs Applications en Physique Mathématique, N 274, Colloques Internationaux C.N.R.S., 1977, pp. 451-457.