Cleft extensions and quotients of twisted quantum doubles

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Given a pair of finite groups F,G and a normalized 3-cocycle ω of G, where F acts on G as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension (formula displayed) where c denotes some suitable cohomological data. When (formula displayed) is a quotient of F by a central subgroup A acting trivially on G, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type (formula displayed). Our construction is particularly natural when F = G acts on G by conjugation, and (formula displayed) is a twisted quantum double Dω(G). In this case, we give necessary and sufficient conditions that Rep(formula displayed) is a modular tensor category.

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Developments in Mathematics

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