Journal article
Strong primeness for equivalence relations arising from Zariski dense subgroups
Proceedings of the London Mathematical Society, Vol.131(1), e70067
07/2025
DOI: 10.1112/plms.70067
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.
Details
- Title: Subtitle
- Strong primeness for equivalence relations arising from Zariski dense subgroups
- Creators
- Daniel Drimbe - University of IowaCyril Houdayer - Université Paris-Saclay
- Resource Type
- Journal article
- Publication Details
- Proceedings of the London Mathematical Society, Vol.131(1), e70067
- DOI
- 10.1112/plms.70067
- ISSN
- 0024-6115
- eISSN
- 1460-244X
- Publisher
- WILEY
- Grant note
- Engineering and Physical Sciences Research Council
This work was initiated when CH was visiting the Mathematical Institute of the University of Oxford during Hilary Term 2024. He is grateful toward Stuart White for his kind invitation. We also thank Adrian Ioana for his valuable comments.
- Language
- English
- Date published
- 07/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984847992902771
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