International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 42, Pages 2231-2264
doi:10.1155/S0161171204308203
Making nontrivially associated modular categories from finite groups
Department of Mathematics, University of Wales, Swansea, Singleton Park, SA2 8PP, UK
Received 15 August 2003
Copyright © 2004 M. M. Al-Shomrani and E. J. Beggs. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).