Frobenius property for fusion categories of small integral dimension

Abstract

Let k be an algebraically closed field of characteristic zero. In this paper, we prove that fusion categories of Frobenius–Perron dimensions 84 and 90 are of Frobenius type. Combining this with previous results in the literature, we obtain that every weakly integral fusion category of Frobenius–Perron dimension less than 120 is of Frobenius type.