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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Projectivity and freeness over comodule algebras
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by Serge Skryabin PDF
Trans. Amer. Math. Soc. 359 (2007), 2597-2623 Request permission

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
  • 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