$C^*$-simplicity, confined subalgebras, and operator algebraic uniform recurrence
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914492353347584 |
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| author | Amrutam, Tattwamasi Jiang, Yongle |
| author_facet | Amrutam, Tattwamasi Jiang, Yongle |
| contents | We introduce the notion of confined subalgebras in the context of the group von Neumann algebra. We also define Uniformly Recurrent States -- an operator-algebraic analog of Uniformly Recurrent Subgroups. Using this framework, we show that a countable discrete group is $C^*$-simple if and only if it admits no non-trivial amenable confined subalgebras. This generalizes the well-known result of Kennedy that characterizes $C^*$-simplicity in terms of trivial amenable uniformly recurrent subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $C^*$-simplicity, confined subalgebras, and operator algebraic uniform recurrence Amrutam, Tattwamasi Jiang, Yongle Operator Algebras Dynamical Systems Functional Analysis General Topology Geometric Topology We introduce the notion of confined subalgebras in the context of the group von Neumann algebra. We also define Uniformly Recurrent States -- an operator-algebraic analog of Uniformly Recurrent Subgroups. Using this framework, we show that a countable discrete group is $C^*$-simple if and only if it admits no non-trivial amenable confined subalgebras. This generalizes the well-known result of Kennedy that characterizes $C^*$-simplicity in terms of trivial amenable uniformly recurrent subgroups. |
| title | $C^*$-simplicity, confined subalgebras, and operator algebraic uniform recurrence |
| topic | Operator Algebras Dynamical Systems Functional Analysis General Topology Geometric Topology |
| url | https://arxiv.org/abs/2604.18458 |