Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425734 | Advances in Mathematics | 2013 | 22 Pages |
Abstract
We generalize Wâ-superrigidity results about Bernoulli actions of rigid groups to general mixing Gaussian actions. We thus obtain the following: If Î is any ICC group which is w-rigid (i.e. it contains an infinite normal subgroup with the relative property (T)) then any mixing Gaussian action Îâ·X is Wâ-superrigid. More precisely, if Îâ·Y is another free ergodic action such that the crossed-product von Neumann algebras are isomorphic Lâ(X)âÎâLâ(Y)âÎ, then the actions are conjugate. We prove a similar statement whenever Î is a non-amenable ICC product of two infinite groups.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Rémi Boutonnet,