W*-superrigidity for cocycle twisted group von Neumann algebras

Abstract

We construct countable groups $G$ with the following new degree of W*-superrigidity: if $L(G)$ is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra $L(\Lambda )$, then the groups $G$ and $\Lambda$ must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary $2$-cocycle. We also give examples of II${}_1$ factors $N$ that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twisted groupoid von Neumann algebra.

arXiv commentv3: minor changes, final version, to appear in Inventiones Mathematicae

References in corpus (2)

• W*-superrigidity for group von Neumann algebras of left-right wreath products
• W*-rigidity paradigms for embeddings of II${}_1$ factors