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Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles

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Abstract

We prove several results concerning quasi-bialgebra morphisms \({\mathcal {D}^{\omega }(G)\to \mathcal {D}^{\eta }(H)}\) of twisted group doubles. We take a particular focus on the isomorphisms which are simultaneously isomorphisms \({\mathcal {D}(G)\to \mathcal {D}(H)}\) and completely determine them. Whenever ω ∈ Z3(G/Z(G), U(1)) this suffices to completely describe \({\text {Aut}(\mathcal {D}^{\omega }(G))}\), the group of quasi-Hopf algebra isomorphisms of \({\mathcal {D}^{\omega }(G)}\), and so generalizes existing descriptions for the case where ω is trivial.

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    Marc Keilberg

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  1. Marc Keilberg
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Correspondence to Marc Keilberg.

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Keilberg, M. Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles. Algebr Represent Theor 23, 1065–1117 (2020). https://doi.org/10.1007/s10468-019-09871-x

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