Projectivity and freeness over comodule algebras

Details Projectivity and freeness over comodule algebras Projectivity and freeness over comodule algebras

2006-10-22

arxiv.org/abs/math/0610657v1

Mathematics

Rings and Algebras

plain tex, 28pp

Scientific paper

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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