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.