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
Recommended Citation
Bruillard, P., Galindo, C., Ng, S., Plavnik, J., Rowell, E., & Wang, Z. (2020). Classification of Super-Modular Categories by Rank. Algebras and Representation Theory, 23 (3), 795-809. https://doi.org/10.1007/s10468-019-09873-9