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.
Revised: January 24, 2017 |
Published: September 1, 2016
Citation
Bruillard P.J., S. Ng, E.C. Rowell, and Z. Wang. 2016.On Classification of Modular Categories by Rank.International Mathematics Research Notices 2016, no. 24:7546-7588.PNNL-SA-111550.doi:10.1093/imrn/rnw020