An intrinsic characterization of C*-simplicity

Abstract

A group is said to be C*-simple if its reduced C*-algebra is simple. We establish an intrinsic (group-theoretic) characterization of groups with this property. Specifically, we prove that a discrete group is C*-simple if and only if it has no non-trivial amenable uniformly recurrent subgroups. We further prove that a group is C*-simple if and only if it satisfies an averaging property considered by Powers.

18 pages; minor changes

References in corpus (2)

• C*-simplicity of free products with amalgamation and radical classes of groups
• A new look at C*-simplicity and the unique trace property of a group

Cited by in corpus (10)

• Noncommutative boundaries and the ideal structure of reduced crossed products
• The Dixmier property and tracial states for C*-algebras
• Stationary C*-dynamical systems
• C*-simplicity of free products with amalgamation and radical classes of groups
• Subgroup dynamics and $C^{\ast }$-simplicity of groups of homeomorphisms
• A generalized Powers averaging property for commutative crossed products
• Relative C*-simplicity and characterizations for normal subgroups
• On simplicity of intermediate C*-algebras
• Uniformly recurrent subgroups and simple $C^{\ast }$-algebras
• On minimal actions of countable groups