W*-superrigidity for cocycle twisted group von Neumann algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910873164972032 |
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| author | Donvil, Milan Vaes, Stefaan |
| author_facet | Donvil, Milan Vaes, Stefaan |
| contents | We construct countable groups $G$ with the following new degree of W*-superrigidity: if $L(G)$ is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra $L(Λ)$, then the groups $G$ and $Λ$ must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary $2$-cocycle. We also give examples of II$_1$ factors $N$ that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twisted groupoid von Neumann algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06053 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | W*-superrigidity for cocycle twisted group von Neumann algebras Donvil, Milan Vaes, Stefaan Operator Algebras Group Theory We construct countable groups $G$ with the following new degree of W*-superrigidity: if $L(G)$ is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra $L(Λ)$, then the groups $G$ and $Λ$ must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary $2$-cocycle. We also give examples of II$_1$ factors $N$ that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twisted groupoid von Neumann algebra. |
| title | W*-superrigidity for cocycle twisted group von Neumann algebras |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2401.06053 |