Algebraic Representations of Ergodic Actions and Super-Rigidity

2013/11/14 by Uri Bader, Bader, Uri, Alex Furman +1
Mathematics · #22E40 (Primary) 22D40 (Secondary) #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1311.3696

openalex publication_date 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• An extension of Margulis' Super-Rigidity Theorem
• Margulis' Super-Rigidity Theorem for non-lattice
• Rigidity theorems for higher rank lattice actions
• Local Rigidity for Cocycles
• Rigidity results for von Neumann algebras arising from mixing extensions of profinite actions of groups on probability spaces