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16 Pages

Quasi‐Hopf Algebras and the Centre of a Tensor Category

WithFlorin Panaite, Freddy Van Oystaeyen

If H is a finite dimensional cocommutative Hopf algebra over the field k and ω : H ⊗ H ⊗ H → k is a nomialized 3‐cocycle in the Sweedler’s cohomology. H x becomes a quasi‐Hopf algebra via ω, which will be denoted by H ω * . We prove that the centre of the tensor category H ω * ‐mod is braided equivalent to the braided tensor category D ω(H)‐mod, where D ω (H) is the quasi‐Hopf algebra introduced in [2] as a generalization of the Dijkgraaf‐Pasquier‐Roche’s quasi‐Hopf algebra D ω(G).