On exactness of group C -algebrass

Quarterly Journal of Mathematics

Volumn 45, Issue 4, 1994, Pages 499-513

  De La Harpe, Pierre ^a   Robertson, A Guyan ^b   Valette, Alain ^c  

^a Section de Mathématiques ^*  (Switzerland)

^b UNIVERSITY OF NEWCASTLE   (Australia)

^c UNIVERSITY OF NEUCHÂTEL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038987787     PISSN: 00335606     EISSN: None     Source Type: Journal    
DOI: 10.1093/qmath/45.4.499     Document Type: Article

References (29)

1. M.-D. Choi and E. Effros, ‘Separable nuclear C*-algebras and injectivity’, Duke Math. J. 43 (1976), 309-322.
2. M.-D. Choi and E. Effros, ‘Nuclear C*-algebra and injectivity: the general case’, Indiana V. Math. J. 26 (1977), 443-446.
3. A. Connes, ‘Classification of injective factors’, Ann. of Math. 103 (1976), 73-115.
4. T. Delzant, ‘Sous-groupes distingufe et quotients des groupes hyperboliques’, Preprint, 1991, IRMA, Strasbourg.
5. J. Dixmier, Les C*-algibres et leurs representations, deux'time edition, Gauthier-Villars 1969.
6. J. M. G. Fell, ‘Weak containment and induced representations of groups’, Canadian J. Math. 14 (1962), 237-268.
7. M. Gromov, ‘Hyperbolic groups’, in Essays in group theory, edited by S. M. Gersten (Springer 1987), 75-263.
8. A. Guichardet, ‘Tensor products of C*-algebras’, Soviet Math. Dokl. 6 (1965), 210-213.
9. P. de la Harpe, A. G. Robertson and A. Valette, ‘On the spectrum of the sum of generators for a finitely generated group’, Israel J. Math 81 (1993) 65-96.
10. P. de la Harpe and A. Valette, ‘La Propriété (T) de Kazhdan pour les groupes localement compacts’, Asterisque 175 (Soc. Math. France 1989).
11. M. Hilsum, J. Renault and G. Skandalis, unpublished work (1991).
12. E. Kirchberg, ‘Positive maps and C*-nuclear algebras’, Proceedings of the International Conference on operator algebras, ideals and their applications in theoretical physics (Leipzig, 1977) pp. 327-328, Teubner, Leipzig 1978.
13. E. Kirchberg, ‘The Fubini theorem for exact C*-algebras’, J. Operator Theory 10 (1983), 3-8.
14. E. Kirchberg, ‘On subalgebras of the CAR algebra’, Preprint, 1990 University Heidelberg J. Functional Analysts, to appear.
15. E. Kirchberg, Letter to A. Valette, Sept. 20, 1990.
16. E. Kirchberg, ‘On non-semisplit extensions, tensor products and exactness of group C*-a!gebras’, Inventiones Math. 112 (1993) 449-489.
17. Lai E. C. Lance, ‘On nuclear C*-algebras’, J. Functional Analysis 12 (1973), 157-176.
18. E. C. Lance, ‘Tensor products and nuclear C*-algebras’, Proc. Symp. Pure Math. 38-1 (Amer. Math. Soc. 1982), 379-399.
19. A. I. Mal’cev, ‘On the faithful representations of infinite groups by matrices’, Amer. Math. Soc. Transl. 45 (1965), 1-18.
20. A. L. T. Paterson, ‘The class of locally compact groups for which C*(G) is amenable’, in Harmonic Analysis, Proc. Luxembourg 1987, P. Eymard and J. P. Piered., Lecture Notes in Math. 1359 (1988), 266-237.
21. G. K. Pedersen, C*-algebras and their automorphism groups, Academic Press 1979.
22. G. Skandalis, ‘Une notion de nucldaritd en /f-theorie (d’aprfes J. Cuntz)’, K-theory 1(1988) 549-573.
23. M. Takesaki, ‘On the cross-norm of the direct product of C*-algebras’, Tdhoku Math. J. 16 (1964), 111-122.
24. M. Takesaki, Theory of operator algebras 1, Springer 1979.
25. J. Tits, ‘Free subgroups in linear groups’, J. of Algebra 20 (1972), 250-270.
26. S. Wassermann, ‘On tensor products of certain group C*-algebras’, J. Functional Analysis 23 (1976), 239-254.
27. S. Wassermann, ‘Tensor products of free-group C*-algebras’, Bull London Math. Soc. 22 (1990), 375-380.
28. S. Wassermann, ‘C*-algebras associated with groups with Kazhdan’s property T Ann. Math. 134 (1991), 423-431.
29. N. R. Wallach, Harmonic analysis on homogeneous spaces, Dekker 1973.