On classification of modular categories by rank

2015/07/18 by Paul Bruillard, Bruillard, Paul, Siu‐Hung Ng +5 · 2 citations
Computer Science · Mathematics · #18D10 #Algebraic structures and combinatorial models #Computability, Logic, AI Algorithms #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1507.05139

openalex publication_date 2015/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=5 modular categories and describe the corresponding monoidal equivalence classes.

Cited by

• Generalized Witt and Morita equivalences
• Modular fusion categories with few twists

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