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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Authors: Galindo, César, Venegas-Ramírez, César F.
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/214199
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Categorical Fermionic Actions and Minimal Modular Extensions. César Galindo and César F. Venegas-Ramírez. SIGMA 21 (2025), 085, 35 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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.
first_indexed 2026-03-21T12:22:07Z
format Article
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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