On relative commutants of subalgebras in group and tracial crossed product von Neumann algebras
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910638009221120 |
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| author | Amrutam, Tattwamasi Bassi, Jacopo |
| author_facet | Amrutam, Tattwamasi Bassi, Jacopo |
| contents | Let $Γ$ be a discrete group acting on a compact Hausdorff space $X$. Given $x\in X$, and $μ\in\text{Prob}(X)$, we introduce the notion of contraction of $μ$ towards $x$ with respect to unitary elements of a group von Neumann algebra not necessarily coming from group elements. Using this notion, we study relative commutants of subalgebras in tracial crossed product von Neumann algebras. The results are applied to negatively curved groups and $\text{SL}(d,\mathbb{Z})$, $d \geq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05948 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On relative commutants of subalgebras in group and tracial crossed product von Neumann algebras Amrutam, Tattwamasi Bassi, Jacopo Operator Algebras Functional Analysis Geometric Topology 46L55, 37A55, 47L65 Let $Γ$ be a discrete group acting on a compact Hausdorff space $X$. Given $x\in X$, and $μ\in\text{Prob}(X)$, we introduce the notion of contraction of $μ$ towards $x$ with respect to unitary elements of a group von Neumann algebra not necessarily coming from group elements. Using this notion, we study relative commutants of subalgebras in tracial crossed product von Neumann algebras. The results are applied to negatively curved groups and $\text{SL}(d,\mathbb{Z})$, $d \geq 2$. |
| title | On relative commutants of subalgebras in group and tracial crossed product von Neumann algebras |
| topic | Operator Algebras Functional Analysis Geometric Topology 46L55, 37A55, 47L65 |
| url | https://arxiv.org/abs/2403.05948 |