On cocycle superrigidity for Gaussian actions
Jesse Peterson, Thomas Sinclair
TL;DR
This paper develops a general framework using von Neumann algebra derivations to analyze cocycle superrigidity in Gaussian actions, providing new proofs, examples, and cohomological conditions for this phenomenon.
Contribution
It introduces a unified approach to cocycle superrigidity for Gaussian actions, extending previous results and identifying new criteria for superrigidity.
Findings
New proofs of existing superrigidity results
Construction of new examples of superrigid Gaussian actions
A cohomological condition for superrigidity based on group representations
Abstract
We present a general setting to investigate U_fin-cocycle superrigidity for Gaussian actions in terms of closable derivations on von Neumann algebras. In this setting we give new proofs to some U_fin-cocycle superrigidity results of S. Popa and we produce new examples of this phenomenon. We also use a result of K. Schmidt to give a necessary cohomological condition on a group representation in order for the resulting Gaussian action to be U_fin-cocycle superrigid.
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