On group theoretical Hopf algebras and exact factorization of finite groups

Details On group theoretical Hopf algebras and exact factorization of finite groups On group theoretical Hopf algebras and exact factorization of finite groups

2002-08-07

arxiv.org/abs/math/0208054v1

Mathematics

Quantum Algebra

10 pages

Scientific paper

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^{omega}(Sigma), for some finite group Sigma and some 3-cocycle omega on Sigma. We show that semisimple Hopf algebras obtained as bicrossed products from an exact factorization of a finite group Sigma are group theoretical. We also describe their Drinfeld double as a twisting of D^{omega}(Sigma), for an appropriate 3-cocycle omega coming from the Kac exact sequence.

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