On Group Theoretical Hopf Algebras and Exact Factorizations of Finite Groups
نویسنده
چکیده
We show that a semisimple Hopf algebra A is group theoretical if and only if its Drinfeld double is a twisting of the Dijkgraaf-Pasquier-Roche quasi-Hopf algebra D(Σ), for some finite group Σ and some ω ∈ Z(Σ, k×). We show that semisimple Hopf algebras obtained as bicrossed products from an exact factorization of a finite group Σ are group theoretical. We also describe their Drinfeld double as a twisting of D(Σ), for an appropriate 3-cocycle ω coming from the Kac exact sequence.
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