Title

On the classification of weakly integral modular categories

Document Type

Article

Publication Date

6-1-2016

Abstract

We classify all modular categories of dimension 4m, where m is an odd square-free integer, and all ranks 6 and 7 weakly integral modular categories. This completes the classification of weakly integral modular categories through rank 7. Our results imply that all integral modular categories of rank at most 7 are pointed (that is, every simple object has dimension 1). All strictly weakly integral (weakly integral but non-integral) modular categories of ranks 6 and 7 have dimension 4m, with m an odd square free integer, so their classification is an application of our main result. The classification of rank 7 integral modular categories is facilitated by an analysis of actions on modular categories by two groups: the Galois group of the field generated by the entries of the S-matrix and the group of isomorphism classes of invertible simple objects. The interplay of these two actions is of independent interest, and we derive some valuable arithmetic consequences from their actions.

Publication Source (Journal or Book title)

Journal of Pure and Applied Algebra

First Page

2364

Last Page

2388

This document is currently not available here.

Share

COinS