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

Abstract

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

Disclosure

“–regular elements p, q with q = psm , and replace (F3) by an escape property together with a matched Fourier-series argument. This suggestion led to Proposi- tion 2.1 and Lemma 2.2, which form the analytic core of the present proof. I used Anthropic’s Claude during the writing of the paper, for discussion of exposition and assistance with language and LATEX. I developed the construction, supplied, and verified all proofs, and checked the mathematical arguments and references, and I take full r”

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2026-08-23T05:10:32.151306Z

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