TUBE REPRESENTATIONS AND TWISTING OF GRADED CATEGORIES

TUBE REPRESENTATIONS AND TWISTING OF GRADED CATEGORIES

We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category C is graded over a group Γ, a torus-valued 3-cocycle on Γ 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 Γ. Combined with...

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Veröffentlicht in:Theory and applications of categories 2018-01, Vol.33 (31), p.964
Hauptverfasser: Bhowmick, Jyotishman, Ghosh, Shamindra, Rakshit, Narayan, Yamashita, Makoto
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Ceramic tubes
Ceramics
Deformation
Polytopes
Tensors
Topology
Toruses
Twisting
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Zusammenfassung:We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category C is graded over a group Γ, a torus-valued 3-cocycle on Γ 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 Γ. 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.
ISSN:1201-561X