Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 085, 35 pages      arXiv:1712.07097      https://doi.org/10.3842/SIGMA.2025.085

Categorical Fermionic Actions and Minimal Modular Extensions

César Galindo and César F. Venegas-Ramírez
Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia

Received March 12, 2025, in final form October 04, 2025; Published online October 13, 2025

Abstract
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 for braided fusion categories with non-Tannakian Müger center involves the fermionic structures and fermionic actions introduced in this work.

Key words: modular categories; minimal modular extensions.

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