Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909223737098240 |
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| author | Borst, Matthijs Caspers, Martijn |
| author_facet | Borst, Matthijs Caspers, Martijn |
| contents | Let $W$ be a finitely generated right-angled Coxeter group with group von Neumann algebra $\mathcal{L}(W)$. We prove the following dichotomy: either $\mathcal{L}(W)$ is strongly solid or $W$ contains $\mathbb{Z} \times \mathbb{F}_2$ as a subgroup. This proves in particular strong solidity of $\mathcal{L}(W)$ for all non-hyperbolic Coxeter groups that do not contain $\mathbb{Z} \times \mathbb{F}_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14988 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra Borst, Matthijs Caspers, Martijn Operator Algebras 46L10 20F55 Let $W$ be a finitely generated right-angled Coxeter group with group von Neumann algebra $\mathcal{L}(W)$. We prove the following dichotomy: either $\mathcal{L}(W)$ is strongly solid or $W$ contains $\mathbb{Z} \times \mathbb{F}_2$ as a subgroup. This proves in particular strong solidity of $\mathcal{L}(W)$ for all non-hyperbolic Coxeter groups that do not contain $\mathbb{Z} \times \mathbb{F}_2$. |
| title | Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra |
| topic | Operator Algebras 46L10 20F55 |
| url | https://arxiv.org/abs/2310.14988 |