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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.13548 |
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| _version_ | 1866915391335301120 |
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| author | Boutonnet, Rémi Houdayer, Cyril |
| author_facet | Boutonnet, Rémi Houdayer, Cyril |
| contents | 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 $Γ< G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $\operatorname{L}(Γ) \subset M \subset \operatorname{L}(Γ\curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13548 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The noncommutative factor theorem for lattices in product groups Boutonnet, Rémi Houdayer, Cyril Operator Algebras Dynamical Systems Group Theory 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 $Γ< G$ in higher rank semisimple algebraic groups. Namely, we give a complete description of all intermediate von Neumann subalgebras $\operatorname{L}(Γ) \subset M \subset \operatorname{L}(Γ\curvearrowright G/P)$ sitting between the group von Neumann algebra and the group measure space von Neumann algebra associated with the action on the Furstenberg-Poisson boundary. |
| title | The noncommutative factor theorem for lattices in product groups |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2207.13548 |