Separable algebras in multitensor C$^*$-categories are unitarizable
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866907844069031936 |
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| author | Giorgetti, Luca Yuan, Wei Zhao, XuRui |
| author_facet | Giorgetti, Luca Yuan, Wei Zhao, XuRui |
| contents | Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C$^*$-category is unitarizable if and only if it is separable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_12019 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Separable algebras in multitensor C$^*$-categories are unitarizable Giorgetti, Luca Yuan, Wei Zhao, XuRui Operator Algebras Category Theory Quantum Algebra 46L89 (Primary) 18M20, 46L08 (Secondary) Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C$^*$-category is unitarizable if and only if it is separable. |
| title | Separable algebras in multitensor C$^*$-categories are unitarizable |
| topic | Operator Algebras Category Theory Quantum Algebra 46L89 (Primary) 18M20, 46L08 (Secondary) |
| url | https://arxiv.org/abs/2312.12019 |