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

Tattwamasi Amrutam

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

Operator Algebras 2026-08-11 v1 Dynamical Systems Functional Analysis General Topology Group Theory

Authors: Tattwamasi Amrutam

Abstract

A discrete group $\Gamma$ has the \emph{ $C^*$ --ISR property} if every unital $\Gamma$ --invariant $C^*$ --subalgebra $A\subseteq C_r^*(\Gamma)$ is of the form $C_r^*(N)$ for a normal subgroup $N\triangleleft\Gamma$ . We show that $\text{PSL}_n(\mathbb{Z})$ satisfies the $C^*$ --ISR property for every $n\geq3$ .

Keywords

C*-algebra invariant subalgebra PSL_n(Z) reduced C*-algebra ISR property discrete group

Cite

@article{arxiv.2608.11127,
  title  = {The $C^*$--ISR Property for $\text{PSL}_n(\mathbb{Z})$},
  author = {Tattwamasi Amrutam},
  journal= {arXiv preprint arXiv:2608.11127},
  year   = {2026}
}

Comments

22 pages; first version. Comments are welcome