On simplicity of reduced C*-algebras of groups

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A countable group is C*-simple if its reduced C*-algebra is a simple algebra. Since Powers recognised in 1975 that non-abelian free groups are C*-simple, large classes of groups which appear naturally in geometry have been identified, including non-elementary Gromov hyperbolic groups and lattices in semisimple groups. In this exposition, C*-simplicity for countable groups is shown to be an extreme case of non-amenability. The basic examples are described and several open problems are formulated.
23 pages

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Operator Algebras, Representation Theory, 22D25; 46L05

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http://salesiana.dossiersoluciones.com/handle/123456789/94705

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0509450
 http://arxiv.org/abs/math/0509450

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arXiv