K-amenability for amalgamated free products of amenable discrete quantum groups

Journal of Functional Analysis

Volumn 212, Issue 1, 2004, Pages 206-221

  Vergnioux, Roland ^a  

^a Institute de Mathématique   (France)

Author keywords

Crossed products; Free products; K theory; Quantum groups

Indexed keywords

EID: 3242665851     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.07.017     Document Type: Article

References (24)

1. Avitzour D. Free products of C*-algebras Trans. Amer. Math. Soc. 271 1982 423-465
2. Baaj S. Représentation régulière du groupe quantique des déplacements de Woronowicz Astérisque 232 1995 11-48
3. Baaj S. Skandalis G. C*-algèbres de Hopf et théorie de Kasparov équivariante K-Theory 2 1989 683-721
4. Baaj S. Skandalis G. Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres Ann. Sci. ENS 26 1993 425-488
5. Banica T. Théorie des représentations du groupe quantique compact libre O(n) C. R. Acad. Sci. Paris 322 1996 241-244
6. Banica T. Symmetries of a generic coaction Math. Ann. 314 1999 763-780
7. Cuntz J. The K-groups for free products of C*-algebras Proc. Sympos. Pure Math. 38 1982 81-84
8. Cuntz J. K-theoretic amenability for discrete groups J. Reine Angew. Math. 344 1983 180-195
9. Germain E. KK-theory of reduced free-product C*-algebras Duke Math. J. 82 1996 707-723
10. E. Germain, Amalgamated free product C*-algebras and KK-theory, in: D. Voiculescu (ed.), Free Probability Theory, Waterloo, ON, 1995, Fields Inst. Commun., Vol. 12, American Mathematical Society, Providence, RI, 1997, 89-103.
11. p) and the action on the associated tree J. Funct. Anal. 58 1984 194-215
12. Kasparov G.G. Skandalis G. Groups acting on buildings, operator K-theory, and Novikov's conjecture K-Theory 4 1991 303-337
13. Kustermans J. Vaes S. Locally compact quantum groups Ann. Sci. ENS 33 2000 837-934
14. Pimsner M. KK-groups of crossed products by groups acting on trees Invent. Math. 86 1986 603-634
15. Pimsner M. Voiculescu D. K-groups of reduced crossed products by free groups J. Oper. Theory 8 1982 131-156
16. 2 Astérisque 46 1977
17. van Daele A. Wang S. Universal quantum groups Internat. J. Math. 7 1996 255-263
18. R. Vergnioux, KK-théorie équivariante et opérateur de Julg-Valette pour les groupes quantiques, Ph.D. Thesis, Université Paris 7, 2002.
19. Voiculescu D. Symmetries of some reduced free product C*-algebras Lecture Notes Math. 1132 1985 556-588
20. Voiculescu D. Dykema K. Nica A. Free Random Variables CRM Montréal Edition 1992 American Mathematical Society Providence, RI
21. Wang S. Free products of compact quantum groups Comm. Math. Phys. 167 1995 671-692
22. Woronowicz S.L. Compact matrix pseudogroups Comm. Math. Phys. 111 1987 613-665
23. Woronowicz S.L. Tannaka-Krein duality for compact matrix pseudogroups, Twisted SU(n) groups Invent. Math. 93 1988 35-76
24. Woronowicz S.L. From multiplicative unitaries to quantum groups Internat. J. Math. 7 1996 127-149