Classification of pivotal tensor categories with fusion rules related to $SO(4)$

Abstract

In this paper we classify all semisimple tensor categories with the same fusion rules as $\mathrm{Rep}(SO(4))$, or one of the associated truncations. We show that such categories are explicitly classified by two non-zero complex numbers. Furthermore we show these tensor categories are always braided, and there exist exactly 8 braidings.

14 pages, comments welcome