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 $\mathrm{L} G$ completely “remembers” the group $G$. More precisely, if $\mathrm{L} G$ is isomorphic to the von Neumann algebra $\mathrm{L} \Lambda$ of an arbitrary countable group $\Lambda$, then $\Lambda$ must be isomorphic to $G$. This represents the first superrigidity result pertaining to group von Neumann algebras.

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Authors

Adrian Ioana

Department of Mathematics, University of California, San Diego, La Jolla, CA 92093

Sorin Popa

Department of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555

Stefaan Vaes

Department of Mathematics, KU Leuven, Celestijnenlaan 200B, B-3001 Leuven
Belgium