On group theoretical Hopf algebras and exact factorization of finite groups
Quantum Algebra
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0208054,
title = {On group theoretical Hopf algebras and exact factorization of finite groups},
author = {Sonia Natale},
journal= {arXiv preprint arXiv:math/0208054},
year = {2007}
}
Comments
10 pages