Groups with simple reduced \(C^*\)-algebras
Consider one infinite conjugacy class group \(\Gamma\) and a subgroup \(\Gamma_0\) of finite index. It is shown that if one of the reduced \(C^*\)-algebras \(C^*_\lambda(\Gamma)\) and \(C^*_\lambda(\Gamma_0)\) is simple, the other is also simple. If one of them has a unique tracial state, the other has such one, too. The main ingredient of the proof is a 1977 theorem of D. Poguntke.
scientific article; zbMATH DE number 1485085