Strong primeness for equivalence relations arising from Zariski dense subgroups

By Cyril Houdayer

Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

In this talk, I will describe an ongoing joint work with Daniel Drimbe in which we show that 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 obtain a unique prime factorization result for direct products of such equivalence relations. This extends and strengthens Zimmer's primeness result for equivalence relations arising from actions of lattices in simple Lie groups (1981). The key novelty in our approach relies on a combination of ergodic theory of algebraic group actions and Popa's intertwining theory for equivalence relations.

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  • DOI 10.57987/IHP.2024.T2.WS3.013
  • Cite this video Houdayer, Cyril (13/06/2024). Strong primeness for equivalence relations arising from Zariski dense subgroups. IHP. Audiovisual resource. DOI: 10.57987/IHP.2024.T2.WS3.013
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