International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 238947 | https://doi.org/10.1155/S0161171204308203

M. M. Al-Shomrani, E. J. Beggs, "Making nontrivially associated modular categories from finite groups", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 238947, 34 pages, 2004. https://doi.org/10.1155/S0161171204308203

Making nontrivially associated modular categories from finite groups

Received15 Aug 2003

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).

Copyright © 2004 Hindawi Publishing Corporation. 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.


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