The noncommutative factor theorem for lattices in product groups

Autor:	Boutonnet, Rémi, Houdayer, Cyril
Rok vydání:	2022
Předmět:	Mathematics - Operator Algebras Mathematics - Dynamical Systems Mathematics - Group Theory
Zdroj:	J. \'Ec. polytech. Math. 10 (2023), 513-524
Druh dokumentu:	Working Paper
Popis:	We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible lattices $\Gamma < G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $\operatorname{L}(\Gamma) \subset M \subset \operatorname{L}(\Gamma \curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary. Comment: 12 pages. To appear in J. \'Ec. polytech. Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.13548 Zobrazit plný text záznamu View this record from Arxiv