A class of superrigid group von Neumann algebras

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.

v3: minor changes, final version, to appear in Annals of Mathematics. v2: improved and clarified exposition

References in corpus (1)

• One-cohomology and the uniqueness of the group measure space decomposition of a II_1 factor

Cited by in corpus (1)

• Type II${}_1$ factors with arbitrary countable endomorphism group