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arXiv · 1801.01735

Tube representations and twisting of graded categories

Jyotishman Bhowmick·Shamindra Ghosh·Narayan Rakshit·Makoto Yamashita
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Abstract

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

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Jyotishman Bhowmick, Shamindra Ghosh, Narayan Rakshit, Makoto Yamashita. 2018-01-05. Tube representations and twisting of graded categories. https://arxiv.org/abs/1801.01735

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