Title

Classification of Super-Modular Categories by Rank

Document Type

Article

Publication Date

6-1-2020

Abstract

We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namely PSU(2)4k+ 2 for k = 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.

Publication Source (Journal or Book title)

Algebras and Representation Theory

First Page

795

Last Page

809

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