W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911102789484544 |
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| author | Drimbe, Daniel Vaes, Stefaan |
| author_facet | Drimbe, Daniel Vaes, Stefaan |
| contents | A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II$_1$ factors. As a consequence, we construct the first uncountable family of discrete groups $Γ$ that are not von Neumann equivalent, which means that their group von Neumann algebras $L(Γ)$ are not W*-correlated, and which implies that these groups are neither measure equivalent, nor have isomorphic or virtually isomorphic group von Neumann algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | W*-correlations of II$_1$ factors and rigidity of tensor products and graph products Drimbe, Daniel Vaes, Stefaan Operator Algebras Group Theory A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II$_1$ factors. As a consequence, we construct the first uncountable family of discrete groups $Γ$ that are not von Neumann equivalent, which means that their group von Neumann algebras $L(Γ)$ are not W*-correlated, and which implies that these groups are neither measure equivalent, nor have isomorphic or virtually isomorphic group von Neumann algebras. |
| title | W*-correlations of II$_1$ factors and rigidity of tensor products and graph products |
| topic | Operator Algebras Group Theory |
| url | https://arxiv.org/abs/2507.04691 |