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Making nontrivially associated modular categories from finite groups

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  • M. M. Al-Shomrani
  • E. J. Beggs

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 ) .

Suggested Citation

  • M. M. Al-Shomrani & E. J. Beggs, 2004. "Making nontrivially associated modular categories from finite groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-34, January.
    • Handle: RePEc:hin:jijmms:238947
    DOI: 10.1155/S0161171204308203
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    Cited by:

    1. Mohammed M. Al-Shomrani & Najla Al-Subaie, 2023. "Graded Rings Associated with Factorizable Finite Groups," Mathematics, MDPI, vol. 11(18), pages 1-14, September.

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