A class of superrigid group von Neumann algebras

2010/07/08 by Adrian Ioana, Ioana, Adrian, Sorin Popa +3 · 6 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1007.1412

Abstract

We prove that for any group G in a fairly large class of generalized wreath product groups, the associated von Neumann algebra L(G) completely "remembers" the group G. More precisely, if L(G) is isomorphic to the von Neumann algebra L(Λ) of an arbitrary countable group Λ, then Λ must be isomorphic to G. This represents the first superrigidity result pertaining to group von Neumann algebras.

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