Making nontrivially associated modular categories from finite groups

M. M. Al-Shomrani and E. J. Beggs

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-34

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 ) .

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:238947

DOI: 10.1155/S0161171204308203

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