Flatness and freeness properties of the generic Hopf Galois extensions

Details Flatness and freeness properties of the generic Hopf Galois extensions Flatness and freeness properties of the generic Hopf Galois extensions

2009-11-19

arxiv.org/abs/0911.3719v3

Rev. Un. Mat. Argentina 51:1 (2010), 79-94

Mathematics

Quantum Algebra

15 pages. Corollary 3.7, Theorem 3.8, missing hypothesis in Theorem 3.13, and one reference added. Misprints corrected.

Scientific paper

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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