A class of superrigid group von Neumann algebras

Details A class of superrigid group von Neumann algebras A class of superrigid group von Neumann algebras

2010-07-08

arxiv.org/abs/1007.1412v2

Mathematics

Operator Algebras

v2: improved and clarified exposition

Scientific paper

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.

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