The $C^{\ast }$--ISR Property for ${\text{PSL}}_n(\mathbb{Z})$

Abstract

A discrete group $\Gamma$ has the \emph{$C^{\ast }$--ISR property} if every unital $\Gamma$--invariant $C^{\ast }$--subalgebra $A\subseteq C_r^{\ast }(\Gamma )$ is of the form $C_r^{\ast }(N)$ for a normal subgroup $N◃\Gamma$. We show that ${\text{PSL}}_n(\mathbb{Z})$ satisfies the $C^{\ast }$--ISR property for every $n\ge 3$.

22 pages; first version. Comments are welcome