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

2025/07/07 by Drimbe, Daniel, Vaes, Stefaan · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2507.04691

Abstract

A variant of Gromov's notion of measure equivalence for groups has been introduced for II₁ factors under different names. We propose the terminology of W*-correlated II₁ factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II₁ 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.

Citations

• Rigid Graph Products
• Biexact von Neumann algebras
• Measure equivalence rigidity via s-malleable deformations
• Properly Proximal von Neumann Algebras
• Von Neumann equivalence and group approximation properties
• Von Neumann equivalence and properly proximal groups
• L₂-cohomology, derivations and quantum Markov semi-groups on q-Gaussian algebras
• Tensor product decompositions and rigidity of full factors
• Unique prime factorization for infinite tensor product factors
• Unique prime factorization and bicentralizer problem for a class of type III factors
• Graph products of operator algebras
• Examples of factors which have no Cartan subalgebras
• Cartan subalgebras of amalgamated free product II₁ factors
• On solid ergodicity for Gaussian actions
• Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1
• On a class of II₁ factors with at most one Cartan subalgebra II
• Factoriality of q-Gaussian von Neumann algebras
• Strong Rigidity of II₁ Factors Arising from Malleable Actions of w-Rigid Groups, I

Cited by

• Universal C^∗-Algebras from Graph Products: Structure and Applications

Related

• Graph products and measure equivalence: classification, rigidity, and quantitative aspects
• Rigidity for graph product von Neumann algebras
• Rigidity for von Neumann algebras of graph product groups. I. Structure of automorphisms
• Strong Rigidity of II₁ Factors Arising from Malleable Actions of w-Rigid Groups, I
• Embedding universality for II₁ factors with property (T)