Categorical Fermionic Actions and Minimal Modular Extensions

2017/12/19 by César Galíndo, Galindo, César, César F. Venegas-Ramírez +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Condensed Matter Physics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1712.07097

openalex publication_date 2017/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

Citations

• On braided fusion categories I
• Anyons in an exactly solved model and beyond
• On the Structure of Modular Categories
• Fermionic modular categories and the 16-fold way

Cited by

• The Classification of 3+1d Symmetry Enriched Topological Order
• Mutual Influence of Symmetries and Topological Field Theories
• Anomalous Actions of Groups on Tensor Categories

Related

• Minimal modular extensions for super-Tannakian categories
• Nondegenerate extensions of near-group braided fusion categories
• On the minimal extension and structure of weakly group-theoretical braided fusion categories
• Computing fusion rules for spherical G-extensions of fusion categories
• Fermionic modular categories and the 16-fold way