Strong primeness for equivalence relations arising from Zariski dense subgroups

Daniel Drimbe; Cyril Houdayer

doi:10.48550/arxiv.2407.01806

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Strong primeness for equivalence relations arising from Zariski dense subgroups

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Strong primeness for equivalence relations arising from Zariski dense subgroups

Daniel Drimbe and Cyril Houdayer

arXiv.org

Cornell University

07/01/2024

DOI: 10.48550/arxiv.2407.01806

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Abstract

We show that orbit equivalence relations arising from essentially free ergodic probability measure preserving actions of Zariski dense discrete subgroups of simple algebraic groups are strongly prime. As a consequence, we prove the existence and the uniqueness of a prime factorization for orbit equivalence relations arising from direct products of higher rank lattices. This extends and strengthens Zimmer's primeness result for equivalence relations arising from actions of lattices in simple Lie groups. The proof of our main result relies on a combination of ergodic theory of algebraic group actions and Popa's intertwining theory for equivalence relations.

Mathematics - Dynamical Systems

Mathematics - Group Theory

Mathematics - Operator Algebras

Details

Title: Subtitle: Strong primeness for equivalence relations arising from Zariski dense subgroups
Creators: Daniel Drimbe
Cyril Houdayer
Resource Type: Preprint
Publication Details: arXiv.org
DOI: 10.48550/arxiv.2407.01806
eISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 07/01/2024
Academic Unit: Mathematics
Record Identifier: 9984696675302771

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