Categorical Fermionic Actions and Minimal Modular Extensions
We define fermionic actions of finite super-groups on fermionic fusion categories and establish necessary and sufficient conditions for their existence. Our main result characterizes when a braided fusion category admits a minimal non-degenerate extension in terms of cohomological obstructions. This...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214199 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Categorical Fermionic Actions and Minimal Modular Extensions. César Galindo and César F. Venegas-Ramírez. SIGMA 21 (2025), 085, 35 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862621774576877568 |
|---|---|
| author | Galindo, César Venegas-Ramírez, César F. |
| author_facet | Galindo, César Venegas-Ramírez, César F. |
| citation_txt | Categorical Fermionic Actions and Minimal Modular Extensions. César Galindo and César F. Venegas-Ramírez. SIGMA 21 (2025), 085, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We define fermionic actions of finite super-groups on fermionic fusion categories and establish necessary and sufficient conditions for their existence. Our main result characterizes when a braided fusion category admits a minimal non-degenerate extension in terms of cohomological obstructions. This characterization of braided fusion categories with non-Tannakian Müger center involves the fermionic structures and fermionic actions introduced in this work.
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| first_indexed | 2026-03-21T12:22:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214199 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:22:07Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Galindo, César Venegas-Ramírez, César F. 2026-02-20T08:01:30Z 2025 Categorical Fermionic Actions and Minimal Modular Extensions. César Galindo and César F. Venegas-Ramírez. SIGMA 21 (2025), 085, 35 pages 1815-0659 2020 Mathematics Subject Classification: 18M20 arXiv:1712.07097 https://nasplib.isofts.kiev.ua/handle/123456789/214199 https://doi.org/10.3842/SIGMA.2025.085 We define fermionic actions of finite super-groups on fermionic fusion categories and establish necessary and sufficient conditions for their existence. Our main result characterizes when a braided fusion category admits a minimal non-degenerate extension in terms of cohomological obstructions. This characterization of braided fusion categories with non-Tannakian Müger center involves the fermionic structures and fermionic actions introduced in this work. We are deeply grateful to the three anonymous referees for their thorough and insightful reports. Their numerous detailed comments and suggestions have significantly improved the clarity of exposition and overall quality of this work. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Categorical Fermionic Actions and Minimal Modular Extensions Article published earlier |
| spellingShingle | Categorical Fermionic Actions and Minimal Modular Extensions Galindo, César Venegas-Ramírez, César F. |
| title | Categorical Fermionic Actions and Minimal Modular Extensions |
| title_full | Categorical Fermionic Actions and Minimal Modular Extensions |
| title_fullStr | Categorical Fermionic Actions and Minimal Modular Extensions |
| title_full_unstemmed | Categorical Fermionic Actions and Minimal Modular Extensions |
| title_short | Categorical Fermionic Actions and Minimal Modular Extensions |
| title_sort | categorical fermionic actions and minimal modular extensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214199 |
| work_keys_str_mv | AT galindocesar categoricalfermionicactionsandminimalmodularextensions AT venegasramirezcesarf categoricalfermionicactionsandminimalmodularextensions |