On classification of modular categories by rank

2015/07/18 by Paul Bruillard, Bruillard, Paul, Siu-Hung Ng +6 · 3 citations
Computer Science · Mathematics · #18D10 #Algebraic structures and combinatorial models #Computability, Logic, AI Algorithms #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras #math.QA #msc:18D10

paper · pdf · doi:10.48550/arxiv.1507.05139

arXiv admin note: substantial text overlap with arXiv:1310.7050

openalex publication_date 2015/07/18 · arxiv created 2016/03/22 · arxiv updated 2016/03/23 · 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.

Citations

• Rank-finiteness for modular categories

Cited by

• Generalized Witt and Morita equivalences
• Modular fusion categories with few twists
• Modular fusion categories with trivial Torelli group actions

Related

• Classification of super-modular categories by rank
• Classification of super-modular categories
• On the classification of non-self-dual modular categories
• Classification of low-rank odd-dimensional modular categories
• A Computational Approach to Classifying Low Rank Modular Categories