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Projectivity and freeness over comodule algebras

Author(s): Serge Skryabin
Journal: Trans. Amer. Math. Soc. 359 (2007), 2597-2623.
MSC (2000): Primary 16W30
Posted: January 25, 2007
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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.

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Additional Information:

Serge Skryabin
Affiliation: Chebotarev Research Institute, Universitetskaya St.~17, 420008 Kazan, Russia
Email: Serge.Skryabin@ksu.ru

DOI: 10.1090/S0002-9947-07-03979-7
PII: S 0002-9947(07)03979-7
Received by editor(s): February 27, 2004
Received by editor(s) in revised form: February 11, 2005
Posted: 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 of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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