Categorical Fermionic Actions and Minimal Modular Extensions
Quantum Algebra
2025-10-15 v3
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 M\"uger center involves the fermionic structures and fermionic actions introduced in this work.
Cite
@article{arxiv.1712.07097,
title = {Categorical Fermionic Actions and Minimal Modular Extensions},
author = {César Galindo and César F. Venegas-Ramírez},
journal= {arXiv preprint arXiv:1712.07097},
year = {2025}
}