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

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...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2024-09, Vol.189, p.103591, Article 103591
Main Authors: Borst, Matthijs, Caspers, Martijn
Format: Article
Language:English
Subjects:
Group von Neumann algebras
Right-angled Coxeter groups
Strong solidity
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Summary: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. Étant donné un groupe de Coxeter à angles droits W et L(W) l'algèbre de von Neumann associée, nous montrons l'alternative suivante : L(W) est fortement solide ou alors Z×F2 est un sous-groupe de W. En particulier, cela implique que les groupes de Coxeter non-hyperboliques qui ne contiennent pas Z×F2 ont une algèbre de von Neumann fortement solide.
ISSN:0021-7824
DOI:10.1016/j.matpur.2024.06.006