In this paper, we show that non-degenerate fusion categories of FP-dimensions p 2 q 3 d and p 3 q 3 d are group-theoretical, where p, q are odd primes, d is a square-free integer such that (pq, d) = 1.

No abstract

We establish a set of general results to study how the Galois action on modular tensor categories interacts with fusion subcategories. This includes a characterization of fusion subcategories of modular tensor categories which are closed under the Galois action, and a classification of modular tensor categories which factor as a product of pointed and transitive categories in terms of pseudoinvertible objects. As an application, we classify modular tensor categories with two Galois orbits of simple objects and a nontrivial grading group.

In this paper, we first show for a slightly degenerate pre-modular fusion category C that squares of dimensions of simple objects divide half of the dimension of C, and that slightly degenerate fusion categories of FP-dimensions 2p n d and 4p n d are nilpotent, where p is an odd prime and d is an odd square-free integer. Then we classify slightly degenerate generalized Tambara-Yamagami fusion categories and weakly integral slightly degenerate fusion categories of particular dimensions.