$C^{\ast }$-simple groups without free subgroups

Abstract

We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^{\ast }$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particular, we show that the reduced $C^{\ast }$-algebra of the free Burnside group $B(m,n)$ of rank $m\ge 2$ and any sufficiently large odd exponent $n$ is simple and has unique trace.

Cited by in corpus (3)

• An intrinsic characterization of C*-simplicity
• Simple reduced $L^p$ operator crossed products with unique trace
• On maximal ideals in certain reduced twisted C*-crossed products