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W∗-correlations of II1 factors and rigidity of tensor products and graph products
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W∗-correlations of II1 factors and rigidity of tensor products and graph products

Daniel Drimbe and Stefaan Vaes
ArXiV.org
Cornell University
07/07/2025
DOI: 10.48550/arxiv.2507.04691
url
https://doi.org/10.48550/arxiv.2507.04691View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

A variant of Gromov's notion of measure equivalence for groups has been introduced for II factors under different names. We propose the terminology of W*-correlated II factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II factors. As a consequence, we construct the first uncountable family of discrete groups that are not von Neumann equivalent, which means that their group von Neumann algebras are not W*-correlated, and which implies that these groups are neither measure equivalent, nor have isomorphic or virtually isomorphic group von Neumann algebras.
Mathematics - Group Theory Mathematics - Operator Algebras

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