Separable algebras in multitensor C$ ^* $-categories are unitarizable
S. Carpi et al. (Comm. Math. Phys., 402 (2023), 169–212) proved that every connected (i.e., haploid) Frobenius algebra in a tensor C$ ^* $-category is unitarizable (i.e., isomorphic to a special C$ ^* $-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024555?viewType=HTML |
| _version_ | 1797219418710736896 |
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| author | Luca Giorgetti Wei Yuan XuRui Zhao |
| author_facet | Luca Giorgetti Wei Yuan XuRui Zhao |
| author_sort | Luca Giorgetti |
| collection | DOAJ |
| description | S. Carpi et al. (Comm. Math. Phys., 402 (2023), 169–212) proved that every connected (i.e., haploid) Frobenius algebra in a tensor C$ ^* $-category is unitarizable (i.e., isomorphic to a special C$ ^* $-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C$ ^* $-category is unitarizable if and only if it is separable. |
| first_indexed | 2024-04-24T12:33:20Z |
| format | Article |
| id | doaj.art-ca400f0c684d4f31a7309c51ad343dae |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T12:33:20Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ca400f0c684d4f31a7309c51ad343dae2024-04-08T01:29:27ZengAIMS PressAIMS Mathematics2473-69882024-03-0195113201133410.3934/math.2024555Separable algebras in multitensor C$ ^* $-categories are unitarizableLuca Giorgetti 0Wei Yuan1XuRui Zhao21. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China 3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, ChinaS. Carpi et al. (Comm. Math. Phys., 402 (2023), 169–212) proved that every connected (i.e., haploid) Frobenius algebra in a tensor C$ ^* $-category is unitarizable (i.e., isomorphic to a special C$ ^* $-Frobenius algebra). Building on this result, we extend it to the non-connected case by showing that an algebra in a multitensor C$ ^* $-category is unitarizable if and only if it is separable.https://www.aimspress.com/article/doi/10.3934/math.2024555?viewType=HTMLmultitensor c$ ^* $-categoryseparable algebraunitarily separable algebrac$ ^* $-frobenius algebraq-system |
| spellingShingle | Luca Giorgetti Wei Yuan XuRui Zhao Separable algebras in multitensor C$ ^* $-categories are unitarizable AIMS Mathematics multitensor c$ ^* $-category separable algebra unitarily separable algebra c$ ^* $-frobenius algebra q-system |
| title | Separable algebras in multitensor C$ ^* $-categories are unitarizable |
| title_full | Separable algebras in multitensor C$ ^* $-categories are unitarizable |
| title_fullStr | Separable algebras in multitensor C$ ^* $-categories are unitarizable |
| title_full_unstemmed | Separable algebras in multitensor C$ ^* $-categories are unitarizable |
| title_short | Separable algebras in multitensor C$ ^* $-categories are unitarizable |
| title_sort | separable algebras in multitensor c categories are unitarizable |
| topic | multitensor c$ ^* $-category separable algebra unitarily separable algebra c$ ^* $-frobenius algebra q-system |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024555?viewType=HTML |
| work_keys_str_mv | AT lucagiorgetti separablealgebrasinmultitensorccategoriesareunitarizable AT weiyuan separablealgebrasinmultitensorccategoriesareunitarizable AT xuruizhao separablealgebrasinmultitensorccategoriesareunitarizable |