C*-simplicity and the amenable radical

Abstract

A countable group is C*-simple if its reduced C*-algebra is simple. It is well known that C*-simplicity implies that the amenable radical of the group must be trivial. We show that the converse does not hold by constructing explicit counter-examples. We additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not C*-simple.

The previous versions of this article were entitled "Discrete groups that are not C*-simple". The results have been strengthened and Theorem D has been added

Cited by in corpus (3)

• The Dixmier property and tracial states for C*-algebras
• Noncommutative Furstenberg boundary
• Uniqueness questions for C*-norms on group rings