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arXiv · 0911.3719

Flatness and freeness properties of the generic Hopf Galois extensions

Christian Kassel·Akira Masuoka
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Abstract

In previous work, to each Hopf algebra H and each invertible right two-cocycle on H, Eli Aljadeff and the first-named author attached a subalgebra B of the free commutative Hopf algebra S generated by the coalgebra underlying H; the algebra B is the subalgebra of coinvariants of a generic Hopf Galois extension. In this paper we give conditions under which S is faithfully flat, or even free, as a B-module. We also show that B is generated as an algebra by certain elements arising from the theory of polynomial identities for comodule algebras developped jointly with Aljadeff.

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Christian Kassel, Akira Masuoka. 2009-11-19. Flatness and freeness properties of the generic Hopf Galois extensions. https://arxiv.org/abs/0911.3719

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