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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.10494 |
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| _version_ | 1866909360939073536 |
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| author | Amrutam, Tattwamasi Hartman, Yair Oppelmayer, Hanna |
| author_facet | Amrutam, Tattwamasi Hartman, Yair Oppelmayer, Hanna |
| contents | We approach the study of sub-von Neumann algebras of the group von Neumann algebra $LΓ$ for countable groups $Γ$ from a dynamical perspective. It is shown that $L(Γ)$ admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of sub-algebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant sub-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10494 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the amenable subalgebras of group von Neumann algebras Amrutam, Tattwamasi Hartman, Yair Oppelmayer, Hanna Operator Algebras Dynamical Systems Functional Analysis Probability 46L10 (Primary) 22D25, 47A35 (Secondary) We approach the study of sub-von Neumann algebras of the group von Neumann algebra $LΓ$ for countable groups $Γ$ from a dynamical perspective. It is shown that $L(Γ)$ admits a maximal invariant amenable subalgebra. The notion of invariant probability measures (IRAs) on the space of sub-algebras is introduced, analogous to the concept of Invariant Random Subgroups. And it is shown that amenable IRAs are supported on the maximal amenable invariant sub-algebra. |
| title | On the amenable subalgebras of group von Neumann algebras |
| topic | Operator Algebras Dynamical Systems Functional Analysis Probability 46L10 (Primary) 22D25, 47A35 (Secondary) |
| url | https://arxiv.org/abs/2309.10494 |