A class of superrigid group von Neumann algebras
Operator Algebras
2012-08-21 v3 Group Theory
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(\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.
Keywords
Cite
@article{arxiv.1007.1412,
title = {A class of superrigid group von Neumann algebras},
author = {Adrian Ioana and Sorin Popa and Stefaan Vaes},
journal= {arXiv preprint arXiv:1007.1412},
year = {2012}
}
Comments
v3: minor changes, final version, to appear in Annals of Mathematics. v2: improved and clarified exposition