On classification of modular categories by rank

Document Type

Article

Publication Date

12-1-2016

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.

Publication Source (Journal or Book title)

International Mathematics Research Notices

First Page

7546

Last Page

7588

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