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 LG completely "remembers" the group G. More precisely, if LG is isomorphic to the von Neumann algebra L of an arbitrary countable group , then must be isomorphic to G. This represents the first superrigidity result pertaining to group von Neumann algebras.