On simplicity of reduced C*-algebras of groups

By Pierre de la Harpe. 2005

113 citations recorded by the source corpus.

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 C*-simple 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 viewed as an extreme case of non-amenability. The basic examples are described, and several open problems are formulated.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/006672031de3d55b0bc161a872af581b68d18fc7

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In Algebra and Number Theory

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Citations in the corpus

An intrinsic characterization of C*-simplicity (2015, background): “[6]), whereas examples of C*-simple groups that do not contain non-abelian free subgroups are now known (see [20] and [16]).”
Boundaries of reduced C*-algebras of discrete groups (2014, background): “In [11], de la Harpe asked if there exists a a countable group which is both C*-simple and does not contain non-abelian free subgroups.”
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces (2011, background): “For a comprehensive survey we refer to [78].”