On slightly degenerate fusion categories

Abstract

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 2pnd and 4pnd are nilpotent, where p is an odd prime and d is an odd square-free integer. Then we classify weakly integral slightly degenerate fusion categories of particular dimensions.