Freeness of Quasi-Hopf Algebras Over Right Coideal Subalgebras

Abstract

We will generalize Skryabin's Freeness Theorem [11]to quasi-Hopf algebras. We will show that for a finite dimensional quasi-Hopf algebra H and a right coideal subalgebra K ⊂ H all (H, K)-quasi Hopf bimodules are free K-modules, in particular, H is a free right and left K-module.

Key Words:

• Coideal subalgebras
• Quasi-Hopf algebras

2000 Mathematics Subject Classification:

• 16W30

ACKNOWLEDGMENTS

I am very grateful to my doctoral supervisor Professor Dr. H.-J. Schneider for his constant support and advice. I would also like to thank the referee for valuable suggestions.

This research was supported by the Elitenetzwerk Bayern.

Notes

Communicated by M. Cohen.