The noncommutative factor theorem for lattices in product groups
Autor: | Boutonnet, Rémi, Houdayer, Cyril |
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Rok vydání: | 2022 |
Předmět: | |
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 |
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