Work

Strong primeness for equivalence relations arising from Zariski dense subgroups

Year: 2025

Type: article

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.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.70067

Authors: Daniel Drimbe, Cyril Houdayer

Institutions: University of Iowa, École Normale Supérieure Paris-Saclay, Université Paris-Saclay, Département de mathématiques et applications

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Institut Universitaire de France, Engineering and Physical Sciences Research Council

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