#
Tube representations and twisting of graded categories

J. Bhowmick, S. Ghosh, N. Rakshit, and M. Yamashita
##

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.

Keywords:
monoidal category, quantum double, tube algebra

2010 MSC:
18D10

*Theory and Applications of Categories,*
Vol. 33, 2018,
No. 31, pp 964-987.

Published 2018-09-23.

http://www.tac.mta.ca/tac/volumes/33/31/33-31.pdf

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