Categorical Fermionic Actions and Minimal Modular Extensions

• 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
• 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

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...