ABSTRACT
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 * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187919/82b7f1d0-8838-4dd2-9241-d60fd25bfe31/content/in11_u001.tif"/> . We prove that the centre of the tensor category H ω * https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187919/82b7f1d0-8838-4dd2-9241-d60fd25bfe31/content/in11_u001.tif"/> ‐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).
