Factoriality of groupoid von Neumann algebras
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916513570619392 |
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| author | Berendschot, Tey Chakraborty, Soham Donvil, Milan Kim, Se-Jin |
| author_facet | Berendschot, Tey Chakraborty, Soham Donvil, Milan Kim, Se-Jin |
| contents | We give a characterisation of factoriality of the groupoid von Neumann algebra $L(\mathcal{G})$ associated to a discrete measured groupoid $(\mathcal{G},μ)$. We introduce the notion of groupoids with `infinite conjugacy classes' and show that this property together with ergodicity of the groupoid is equivalent to factoriality of $L(\mathcal{G})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factoriality of groupoid von Neumann algebras Berendschot, Tey Chakraborty, Soham Donvil, Milan Kim, Se-Jin Operator Algebras 46L10, 20L05 We give a characterisation of factoriality of the groupoid von Neumann algebra $L(\mathcal{G})$ associated to a discrete measured groupoid $(\mathcal{G},μ)$. We introduce the notion of groupoids with `infinite conjugacy classes' and show that this property together with ergodicity of the groupoid is equivalent to factoriality of $L(\mathcal{G})$. |
| title | Factoriality of groupoid von Neumann algebras |
| topic | Operator Algebras 46L10, 20L05 |
| url | https://arxiv.org/abs/2402.04449 |