Projectivity and freeness over comodule algebras
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Abstract:
Let $H$ be a Hopf algebra and $A$ an $H$-simple right $H$-comodule algebra. It is shown that under certain hypotheses every $(H,A)$-Hopf module is either projective or free as an $A$-module and $A$ is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for $H$-simple $H$-module algebras.References
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Additional Information
- Serge Skryabin
- Affiliation: Chebotarev Research Institute, Universitetskaya St. 17, 420008 Kazan, Russia
- MR Author ID: 246155
- Email: Serge.Skryabin@ksu.ru
- Received by editor(s): February 27, 2004
- Received by editor(s) in revised form: February 11, 2005
- Published electronically: January 25, 2007
- Additional Notes: This research was supported by the project “Construction and applications of non-commutative geometry" from FWO Vlaanderen. I would like to thank the Free University of Brussels VUB for their hospitality during the time the work was conducted.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 2597-2623
- MSC (2000): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9947-07-03979-7
- MathSciNet review: 2286047