On simplicity of reduced C*-algebras of groups

Details On simplicity of reduced C*-algebras of groups On simplicity of reduced C*-algebras of groups

2005-09-20

arxiv.org/abs/math/0509450v1

Mathematics

Operator Algebras

23 pages

Scientific paper

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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