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

Matthijs Borst; Martijn Caspers

doi:10.1016/j.matpur.2024.06.006

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

Matthijs Borst, Martijn Caspers^*

^*Corresponding author for this work

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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.

Original language	English
Article number	103591
Journal	Journal des Mathematiques Pures et Appliquees
Volume	189
DOIs	https://doi.org/10.1016/j.matpur.2024.06.006
Publication status	Published - 2024

Keywords

Group von Neumann algebras
Right-angled Coxeter groups
Strong solidity

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10.1016/j.matpur.2024.06.006

1-s2.0-S0021782424000813-mainFinal published version, 422 KBLicence: CC BY

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title = "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.",

keywords = "Group von Neumann algebras, Right-angled Coxeter groups, Strong solidity",

author = "Matthijs Borst and Martijn Caspers",

year = "2024",

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AU - Borst, Matthijs

AU - Caspers, Martijn

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AB - 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.

KW - Group von Neumann algebras

KW - Right-angled Coxeter groups

KW - Strong solidity

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U2 - 10.1016/j.matpur.2024.06.006

DO - 10.1016/j.matpur.2024.06.006

M3 - Article

AN - SCOPUS:85199788604

SN - 0021-7824

VL - 189

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

M1 - 103591

ER -

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

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