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

Abstract

In this paper we classify all semisimple pivotal tensor categories with the same fusion rules as 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 aside from a small number of degenerate cases, there exist exactly 8 braidings.