Uniqueness of almost periodic outer flows on the hyperfinite type $\mathrm{II}_1$ factor
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917486351351808 |
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| author | Houdayer, Cyril Marrakchi, Amine |
| author_facet | Houdayer, Cyril Marrakchi, Amine |
| contents | We show that any almost periodic outer flow $α: \mathbb R \curvearrowright R$ on the hyperfinite type $\mathrm{II}_1$ factor with Connes' spectrum $Γ(α) = \mathbb R$ satisfies the Rokhlin property and thus is unique up to cocycle conjugacy. The proof relies on a key cocycle perturbation result for type $\mathrm{III}$ amenable equivalence relations. As a byproduct of our methods, we also show that every almost periodic factor of type $\mathrm{III}_1$ with separable predual has an extremal almost periodic faithful normal state. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02781 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of almost periodic outer flows on the hyperfinite type $\mathrm{II}_1$ factor Houdayer, Cyril Marrakchi, Amine Operator Algebras Dynamical Systems 37A20, 37A40, 46L10, 46L36, 46L55 We show that any almost periodic outer flow $α: \mathbb R \curvearrowright R$ on the hyperfinite type $\mathrm{II}_1$ factor with Connes' spectrum $Γ(α) = \mathbb R$ satisfies the Rokhlin property and thus is unique up to cocycle conjugacy. The proof relies on a key cocycle perturbation result for type $\mathrm{III}$ amenable equivalence relations. As a byproduct of our methods, we also show that every almost periodic factor of type $\mathrm{III}_1$ with separable predual has an extremal almost periodic faithful normal state. |
| title | Uniqueness of almost periodic outer flows on the hyperfinite type $\mathrm{II}_1$ factor |
| topic | Operator Algebras Dynamical Systems 37A20, 37A40, 46L10, 46L36, 46L55 |
| url | https://arxiv.org/abs/2605.02781 |