On classification of modular categories by rank

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.

arXiv admin note: substantial text overlap with arXiv:1310.7050

References in corpus (1)

• From Quantum Groups to Unitary Modular Tensor Categories

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