On classification of modular categories by rank

By P. Bruillard, Siu-Hung Ng, Eric C. Rowell, Zhenghan Wang. 2015

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/885df79063c72d067416439600a230dcaae542fb