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

2023/10/23 by Matthijs Borst, Martijn Caspers, Borst, Matthijs +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2310.14988

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 × \mathbbF₂ as a subgroup. This proves in particular strong solidity of L(W) for all non-hyperbolic Coxeter groups that do not contain ℤ × \mathbbF₂.

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• Strong solidity classification of Coxeter groups
• Universal C^∗-Algebras from Graph Products: Structure and Applications

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