Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra

Abstract

Let W be a finitely generated right-angled Coxeter group with group von Neumann algebra $L\left(W\right)$. We prove the following dichotomy: either $L\left(W\right)$ is strongly solid or W contains $Z\times F_2$ as a subgroup. This proves in particular strong solidity of $L\left(W\right)$ for all non-hyperbolic Coxeter groups that do not contain $Z\times F_2$.