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On simplicity of reduced C*-algebras of groups

Pierre de la Harpe
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Abstract

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.

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Pierre de la Harpe. 2005-09-20. On simplicity of reduced C*-algebras of groups. https://arxiv.org/abs/math/0509450

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