A new look at C*-simplicity and the unique trace property of a group

Abstract

We characterize when the reduced C*-algebra of a group has unique tracial state, respectively, is simple, in terms of Dixmier-type properties of the group C*-algebra. We also give a simple proof of the recent result by Breuillard, Kalantar, Kennedy and Ozawa that the reduced C*-algebra of a group has unique tracial state if and only if the amenable radical of the group is trivial.

8 pages

Cited by in corpus (6)

• The Dixmier property and tracial states for C*-algebras
• An intrinsic characterization of C*-simplicity
• Subgroup dynamics and $C^{\ast }$-simplicity of groups of homeomorphisms
• Existence of tracial states on reduced group C*-algebras
• On simplicity of intermediate C*-algebras
• On Intermediate $C^{\ast }$-subalgebras of $C^{\ast }$-simple Group Actions