Hypertrace and entropy gap characterizations of property (T) for $\mathrm{II}_1$ factors
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913380399316992 |
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| author | Zhou, Shuoxing |
| author_facet | Zhou, Shuoxing |
| contents | We establish a hypertrace characterization of property (T) for $\mathrm{II}_1$ factors: Given a $\mathrm{II}_1$ factors $M$, $M$ does not have property (T) if and only if there exists a von Neumann algebra $\mathcal{A}$ with $M\subset \mathcal{A}$ such that $\mathcal{A}$ admits a $M$-hypertrace but no normal hypertrace. For $M$ without property (T), such an inclusion $M\subset \mathcal{A}$ also admits almost vanishing Furstenberg entropy. With the same construction of $M\subset \mathcal{A}$, we also establish similar characterizations of Haagerup property for $\mathrm{II}_1$ factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15110 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hypertrace and entropy gap characterizations of property (T) for $\mathrm{II}_1$ factors Zhou, Shuoxing Operator Algebras Dynamical Systems Group Theory We establish a hypertrace characterization of property (T) for $\mathrm{II}_1$ factors: Given a $\mathrm{II}_1$ factors $M$, $M$ does not have property (T) if and only if there exists a von Neumann algebra $\mathcal{A}$ with $M\subset \mathcal{A}$ such that $\mathcal{A}$ admits a $M$-hypertrace but no normal hypertrace. For $M$ without property (T), such an inclusion $M\subset \mathcal{A}$ also admits almost vanishing Furstenberg entropy. With the same construction of $M\subset \mathcal{A}$, we also establish similar characterizations of Haagerup property for $\mathrm{II}_1$ factors. |
| title | Hypertrace and entropy gap characterizations of property (T) for $\mathrm{II}_1$ factors |
| topic | Operator Algebras Dynamical Systems Group Theory |
| url | https://arxiv.org/abs/2312.15110 |