International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 41-44, Pages 2231-2264
doi:10.1155/S0161171204308203

Making nontrivially associated modular categories from finite groups

Abstract

We show that the double 𝒟 of the nontrivially associated tensor category constructed from left coset representatives of a subgroup of a finite group X is a modular category. Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. This definition is shown to be adjoint invariant and multiplicative on tensor products. A detailed example is given. Finally, we show an equivalence of categories between the nontrivially associated double 𝒟 and the trivially associated category of representations of the Drinfeld double of the group D(X).