An intrinsic characterization of C*-simplicity

By M. Kennedy. Annales Scientifiques de l'Ecole Normale Supérieure, 2015

63 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1d6356d872910ec8431d41c55128c54f87ca1cca