On cocycle superrigidity for Gaussian actions

By J. Peterson, Thomas Sinclair. Ergodic Theory and Dynamical Systems, 2009

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Abstract We present a general setting to investigate 𝒰fin-cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this setting we give new proofs to some 𝒰fin-cocycle superrigidity results of S. Popa and we produce new examples of this phenomenon. We also use a result of K. R. Parthasarathy and K. Schmidt to give a necessary cohomological condition on a group representation in order for the resulting Gaussian action to be 𝒰fin-cocycle superrigid.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8b6b719d2d0ef46adacc9c500b32436bde031038

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

RIGIDITY FOR VON NEUMANN ALGEBRAS (2017, background): “in the property (T) case, see also [Fu06,Va06a]. In addition to property (T) and product groups, Theorem 5.1 has been shown to hold for groups Γ such that L(Γ) is L2-rigid in the sense of [Pe06] (see [PS09]) and for inner amenable non-amenable groups Γ (see [TD14]). The following problem due to Popa”
Classification and rigidity for von Neumann algebras (2012, background): “also [Po86, Po06c] for the construction of a malleable deformation for the free group factors. Example 3.6. Next, we recall the construction of a malleable deformation from cocycles ([Si10], see also [PS09]). Start with a countable group Γ, an orthogonal representation π : Γ →O(H) onto a separable r”
Strong solidity of group factors from lattices in SO(n,1) and SU(n,1) (2010, methodology): “e have obtained a “hypertrace” characterization of amenability for correspondences in Theorem 2.2, the result follows by the same arguments as in Lemma 2.2 in [7]. Deﬁnition 2.5 (cf. Deﬁnition 1.3 in [18]). Let M be a II1 factor, H an M-M correspondence and Pc the orthogonal projection onto the subs”