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W*-superrigidity for groups with infinite center

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arxiv 2410.13417 v3 pith:SLAGSUEK submitted 2024-10-17 math.OA math.GR

Milan Donvil , Stefaan Vaes This is my paper · ORCID
classification math.OAmath.GR
keywords groupscenterresultsrigiditygroupinfiniteisomorphismsneumann
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abstract

We construct discrete groups $G$ with infinite center that are nevertheless W*-superrigid, meaning that the group von Neumann algebra $L(G)$ fully remembers the group $G$. We obtain these rigidity results both up to isomorphisms and up to virtual isomorphisms of the groups and their von Neumann algebras. Our methods combine rigidity results for the quotient of these groups by their center with rigidity results for their 2-cohomology.

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  1. Non-uniform higher-rank lattices are character rigid

    math.GR 2025-07 accept novelty 8.0 of 10

    Every irreducible non-uniform lattice in a higher-rank semisimple group of characteristic not 2 is character rigid.

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