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(W). We prove the following dichotomy: either L(W) is strongly solid or W contains Z×F2 as a subgroup. This proves in particular strong solidity of L(W) for all non-hyperbolic Coxeter groups that do not contain Z×F2.