Algebraic Representations of Ergodic Actions and Super-Rigidity

Abstract

We revisit Margulis-Zimmer Super-Rigidity and provide some generalizations. In particular we obtain super-rigidity results for lattices in higher-rank groups or product of groups, targeting at algebraic groups over arbitrary fields with absolute values. We also obtain cocycle super-rigidity results for a wide class of groups with respect to mixing actions. Our approach is based on a systematic study of algebraic representations of ergodic actions.

25 pages. The file is different from a previously distributed file by the same name. 2nd submission: an inaccuracy in the definition of a morphism of bi-algebraic representations was fixed