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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finiteness of the number of coideal subalgebras
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by Serge Skryabin PDF
Proc. Amer. Math. Soc. 145 (2017), 2859-2869 Request permission

Abstract:

It is proved that any finite dimensional Hopf algebra which is either semisimple or cosemisimple has finitely many right coideal subalgebras. As a consequence, over an algebraically closed base field any action of a finite dimensional cosemisimple Hopf algebra on a commutative domain factors through an action of a group algebra. This extends two results of Etingof and Walton to the case where the Hopf algebra is cosemisimple, but not necessarily semisimple.
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Additional Information
  • Serge Skryabin
  • Affiliation: Institute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya Street 18, 420008 Kazan, Russia
  • MR Author ID: 246155
  • Email: Serge.Skryabin@kpfu.ru
  • Received by editor(s): January 11, 2016
  • Received by editor(s) in revised form: August 24, 2016
  • Published electronically: December 8, 2016
  • Communicated by: Kailash Misra
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2859-2869
  • MSC (2010): Primary 16T05
  • DOI: https://doi.org/10.1090/proc/13463
  • MathSciNet review: 3637936