تقرير
On invariant subalgebras of group $C^*$ and von Neumann algebras
| العنوان: | On invariant subalgebras of group $C^*$ and von Neumann algebras |
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| المؤلفون: | Kalantar, Mehrdad, Panagopoulos, Nikolaos |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras |
| الوصف: | Given an irreducible lattice $\Gamma$ in the product of higher rank simple Lie groups, we prove a co-finiteness result for the $\Gamma$-invariant von Neumann subalgebras of the group von Neumann algebra $\mathcal{L}(\Gamma)$, and for the $\Gamma$-invariant unital $C^*$-subalgebras of the reduced group $C^*$-algebra $C^*_{\rm red}(\Gamma)$. We use these results to show that: (i) every $\Gamma$-invariant von Neumann subalgebra of $\mathcal{L}(\Gamma)$ is generated by a normal subgroup; and (ii) given a non-amenable unitary representation $\pi$ of $\Gamma$, every $\Gamma$-equivariant conditional expectation on $C^*_\pi(\Gamma)$ is the canonical conditional expectation onto the $C^*$-subalgebra generated by a normal subgroup. Comment: Changes to version 2: the statement of Theorem 1.2 improved. 16 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2108.02928 |
| رقم الأكسشن: | edsarx.2108.02928 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |