Making nontrivially associated modular categories from finite groups

Abstract

We show that the non-trivially associated tensor category constructed from left coset representatives of a subgroup of a finite group is a modular category. Also we give a definition of the character of an object in a ribbon category which is the category of representations of a braided Hopf algebra in the category. The definition is shown to be adjoint invariant and multiplicative. A detailed example is given. Finally we show an equivalence of categories between the non-trivially associated double D and the category of representations of the double of the group D(X).