Finiteness of the number of coideal subalgebras

Skryabin, Serge

doi:10.1090/proc/13463

Finiteness of the number of coideal subalgebras
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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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