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Discrete groups and simple C*-algebras

Published online by Cambridge University Press:  24 October 2008

Erik Bédos
Erik Bédos
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo 3, Norway
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Extract

Let G denote a discrete group and let us say that G is C*-simple if the reduced group C*-algebra associated with G is simple. We notice immediately that there is no interest in considering here the full group C*-algebra associated with G, because it is simple if and only if C is trivial. Since Powers in 1975 [26] proved that all nonabelian free groups are C*-simple, the class of C*-simp1e groups has been considerably enlarged (see [1, 2, 6, 7, 12, 13, 14, 16, 24] as a sample!), and two important subclasses are so-called weak Powers groups ([6, 13]; see Section 4 for definition and examples) and the groups of Akemann-Lee type [1, 2], which are groups possessing a normal non-abelian free subgroup with trivial centralizer.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 3 , May 1991 , pp. 521 - 537
Copyright
Copyright © Cambridge Philosophical Society 1991

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