Freeness of Quasi-Hopf Algebras over Coideal Subalgebras
Hannah Henker (Munich)
Wednesday 12th November, 2008 16:00-17:00 214
The Nichols-Zoeller Freeness Theorem, which states the freeness of nite dimen- sional Hopf algebras over their Hopf subalgebras, can be seen as the analogon to Lagrange's Theorem in group theory. Since the natural sub-objects of a Hopf algebra are the right and left coideal subalgebras rather then the Hopf subalge- bras, it was a great achievement when Skryabin succeeded in proving that Hopf algebras are also free over their coideal subalgebras. We will generalize Skryabins Freeness Theorem to quasi-Hopf algebras, as introduced by Drinfel'd. More precisely, we prove that for a nite dimensional quasi-Hopf algebra H and a right coideal subalgebra K of H, all (H;K)-quasi Hopf bimodules are free K-modules and K is a Frobenius algebra.