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Abstract
The notions of Galois and cleft extensions are generalized for coquasi-Hopf algebras. It is shown that an extension over a coquasi-Hopf algebra is cleft if and only if it is Galois and has the normal basis property. A Schneider type theorem [Citation34] is proven for coquasi-Hopf algebras with bijective antipode. As an application, we generalize Schauenburg's bialgebroid construction for coquasi-Hopf algebras.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The first part of this article was written while the author participated to the Socrates Intensive Program “Geometric and Algebraic Methods with Applications in Physics,” held at the University of Antwerpen, Belgium, in September 2007. Many thanks to the Department of Mathematics (UA) for their warm hospitality. The author would also like to express her gratitude to Prof. C. Năstăsescu and F. Panaite for helpful discussions, which improved this article.
Notes
Communicated by M. Cohen.