This study defines fermionic actions and characterizes minimal extensions in fusion categories, indicating core cohomological conditions.
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.
No takes yet. Share an insight, caveat, or question.
Galíndo et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: