Elementary embeddings into ultrapower $\mathrm{II}_1$ factors without a UCP lift
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918243168419840 |
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| author | Gao, David Jekel, David |
| author_facet | Gao, David Jekel, David |
| contents | We show that there are $\mathrm{II}_1$ factors $M$ and elementary embeddings $M \to M^{\mathcal{U}}$ which do not lift to sequences of UCP maps, and in fact $M$ can be chosen from any given elementary equivalence class. Furthermore, under continuum hypothesis, we show that in the sense of cardinality "most" automorphisms of a ultrapower $M^{\mathcal{U}}$ of a separable $\mathrm{II}_1$ factor do not lift to a sequence of UCP maps $φ_n: M \to M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10129 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elementary embeddings into ultrapower $\mathrm{II}_1$ factors without a UCP lift Gao, David Jekel, David Operator Algebras Logic 46L10, 03C66, 03C20 We show that there are $\mathrm{II}_1$ factors $M$ and elementary embeddings $M \to M^{\mathcal{U}}$ which do not lift to sequences of UCP maps, and in fact $M$ can be chosen from any given elementary equivalence class. Furthermore, under continuum hypothesis, we show that in the sense of cardinality "most" automorphisms of a ultrapower $M^{\mathcal{U}}$ of a separable $\mathrm{II}_1$ factor do not lift to a sequence of UCP maps $φ_n: M \to M$. |
| title | Elementary embeddings into ultrapower $\mathrm{II}_1$ factors without a UCP lift |
| topic | Operator Algebras Logic 46L10, 03C66, 03C20 |
| url | https://arxiv.org/abs/2512.10129 |