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Finiteness of the number of coideal subalgebras


Author: Serge Skryabin
Journal: Proc. Amer. Math. Soc. 145 (2017), 2859-2869
MSC (2010): Primary 16T05
DOI: https://doi.org/10.1090/proc/13463
Published electronically: December 8, 2016
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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
Email: Serge.Skryabin@kpfu.ru

DOI: https://doi.org/10.1090/proc/13463
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
Article copyright: © Copyright 2016 American Mathematical Society