Geodesic
Tube representations and twisting of graded categories
Theory and applications of categories, Tome 33 (2018), pp. 964-987

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We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category $C$ is graded over a group $\Gammaa$, a torus-valued 3-cocycle on $\Gammaa$ can be used to deform the associator of $C$. We show that it induces a 2-cocycle on the groupoid of the adjoint action of $\Gammaa$. Combined with the natural Fell bundle structure of tube algebra over this groupoid, we show that the tube algebra of the twisted category is a 2-cocycle twisting of the original one.

Publié le :
Classification : 18D10
Keywords: monoidal category, quantum double, tube algebra 
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     author = {J. Bhowmick and S. Ghosh and N. Rakshit and M. Yamashita},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2018_33_a30/}
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J. Bhowmick; S. Ghosh; N. Rakshit; M. Yamashita. Tube representations and twisting of graded categories. Theory and applications of categories, Tome 33 (2018), pp. 964-987. http://geodesic.mathdoc.fr/item/TAC_2018_33_a30/