# On cocycle superrigidity for Gaussian actions

## 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.

## Key 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.