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On classification of modular categories by rank
Published 18 Jul 2015 in math.QA | (1507.05139v2)
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.
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