A class of superrigid group von Neumann algebras


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.


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