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Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles

  • Marc KeilbergEmail author
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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 ωZ3(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.

Keywords

Finite groups Drinfeld double Automorphisms Quasi-Hopf algebras Quasibialgebras 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Los AngelesUSA

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