On Simplicity of Reduced C∗-algebras of Groups
نویسندگان
چکیده
A countable group is C∗-simple if its reeduced 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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