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On cocycle superrigidity for Gaussian actions

Published online by Cambridge University Press:  10 June 2011

JESSE PETERSON  and
THOMAS SINCLAIR
JESSE PETERSON
Affiliation:
Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA (email: jesse.d.peterson@vanderbilt.edu, thomas.sinclair@vanderbilt.edu)
THOMAS SINCLAIR
Affiliation:
Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA (email: jesse.d.peterson@vanderbilt.edu, thomas.sinclair@vanderbilt.edu)
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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.

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Type
Research Article
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Ergodic Theory and Dynamical Systems , Volume 32 , Issue 1 , February 2012 , pp. 249 - 272
Copyright
Copyright © Cambridge University Press 2011

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