English

On classification of modular categories by rank

Quantum Algebra 2016-03-23 v2

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=55 modular categories and describe the corresponding monoidal equivalence classes.

Keywords

Cite

@article{arxiv.1507.05139,
  title  = {On classification of modular categories by rank},
  author = {Paul Bruillard and Siu-Hung Ng and Eric C. Rowell and Zhenghan Wang},
  journal= {arXiv preprint arXiv:1507.05139},
  year   = {2016}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1310.7050

R2 v1 2026-06-22T10:14:17.030Z