Classification of Certain Weakly Integral Fusion Categories
摘要
The author proves that braided fusion categories of Frobenius-Perron dimension pmqnd or p2q2r2 are weakly group-theoretical, where p, q, r are distinct prime numbers, d is a square-free natural number such that (pq, d) = 1. As an application, the author obtains that weakly integral braided fusion categories of Frobenius-Perron dimension less than 1800 are weakly group-theoretical, and weakly integral braided fusion categories of odd dimension less than 33075 are solvable. For the general case, the author proves that fusion categories (not necessarily braided) of Frobenius-Perron dimension 84 and 90 are either solvable or group-theoretical. Together with the results in the literature, this shows that every weakly integral fusion category of Frobenius-Perron dimension less than 120 is either solvable or group-theoretical. Thus the author completes the classification of all these fusion categories in terms of Morita equivalence.