Selfless reduced $C^{\ast }$-algebras of linear groups

Abstract

It is shown that the reduced C*-algebra of a nontrivial linear group $\hat{I}“<G{L}_d(k)$ with trivial amenable radical is selfless. Thus selflessness and simplicity coincide for reduced C*-algebras of linear groups. Similar results are obtained for twisted reduced group C*-algebra.

v1: correct a typo in one of the main theorems v2: several corrections following referee report. To appear in Proc. Lond. Math. Soc