Module Categories of the Generic Virasoro VOA and Quantum Groups
In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213197 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Module Categories of the Generic Virasoro VOA and Quantum Groups. Shinji Koshida. SIGMA 21 (2025), 039, 26 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862655718904037376 |
|---|---|
| author | Koshida, Shinji |
| author_facet | Koshida, Shinji |
| citation_txt | Module Categories of the Generic Virasoro VOA and Quantum Groups. Shinji Koshida. SIGMA 21 (2025), 039, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group (₂) with determined by the central charge. This is a continuation of our previous work in which we examined intertwining operators for the generic Virasoro VOA in detail. Our strategy to show the categorical equivalence is to take those results as input and directly compare the structures of tensor categories. Therefore, we are to execute the most elementary proof of categorical equivalence. We also study the category of ₁-cofinite modules of the generic Virasoro VOA. We show that it is ribbon equivalent to the category of finite-dimensional type I modules of (₂) ⊗ ~(₂), where and ~ are again related to the central charge.
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| first_indexed | 2026-03-15T20:34:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213197 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T20:34:30Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Koshida, Shinji 2026-02-16T16:38:29Z 2025 Module Categories of the Generic Virasoro VOA and Quantum Groups. Shinji Koshida. SIGMA 21 (2025), 039, 26 pages 1815-0659 2020 Mathematics Subject Classification: 17B69; 17B68; 18M15 arXiv:2207.12969 https://nasplib.isofts.kiev.ua/handle/123456789/213197 https://doi.org/10.3842/SIGMA.2025.039 In this paper, we prove the equivalence between two ribbon tensor categories. On the one hand, we consider the category of modules of the Virasoro vertex operator algebra with generic central charge (generic Virasoro VOA) generated by those simple modules lying in the first row of the Kac table. On the other hand, we take the category of finite-dimensional type I modules of the quantum group (₂) with determined by the central charge. This is a continuation of our previous work in which we examined intertwining operators for the generic Virasoro VOA in detail. Our strategy to show the categorical equivalence is to take those results as input and directly compare the structures of tensor categories. Therefore, we are to execute the most elementary proof of categorical equivalence. We also study the category of ₁-cofinite modules of the generic Virasoro VOA. We show that it is ribbon equivalent to the category of finite-dimensional type I modules of (₂) ⊗ ~(₂), where and ~ are again related to the central charge. The author is grateful to Kalle Kytölä, Eveliina Peltola, and Ingo Runkel for fruitful discussions. The author also thanks the anonymous referees for their various suggestions for improvement. This work was supported by the Academy of Finland (No. 248 130). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Module Categories of the Generic Virasoro VOA and Quantum Groups Article published earlier |
| spellingShingle | Module Categories of the Generic Virasoro VOA and Quantum Groups Koshida, Shinji |
| title | Module Categories of the Generic Virasoro VOA and Quantum Groups |
| title_full | Module Categories of the Generic Virasoro VOA and Quantum Groups |
| title_fullStr | Module Categories of the Generic Virasoro VOA and Quantum Groups |
| title_full_unstemmed | Module Categories of the Generic Virasoro VOA and Quantum Groups |
| title_short | Module Categories of the Generic Virasoro VOA and Quantum Groups |
| title_sort | module categories of the generic virasoro voa and quantum groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213197 |
| work_keys_str_mv | AT koshidashinji modulecategoriesofthegenericvirasorovoaandquantumgroups |