Hilbert--Schmidt stability for graph products

TL;DR

This paper proves that certain graph products of abelian groups and $C^*$-algebras, specifically those on chordal graphs, are stable under Hilbert--Schmidt perturbations, including right-angled Artin groups.

Contribution

It establishes Hilbert--Schmidt stability for graph products on chordal graphs, a class not previously known to have this property.

Findings

Hilbert--Schmidt stability for graph products of abelian groups

Stability results for $C^*$-algebras on chordal graphs

Right-angled Artin groups are Hilbert--Schmidt stable

Abstract

In this short note we prove Hilbert--Schmidt stability for graph products of abelian groups and $C^*$-algebras on chordal graphs. In particular, this shows that right-angled Artin groups on chordal graphs are Hilbert--Schmidt stable.