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arXiv · 2507.04691

W*-correlations of II$_1$ factors and rigidity of tensor products and graph products

Daniel Drimbe·Stefaan Vaes
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Abstract

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.

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Daniel Drimbe, Stefaan Vaes. 2025-08-12. W*-correlations of II$_1$ factors and rigidity of tensor products and graph products. https://arxiv.org/abs/2507.04691

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