Resumen de Flatness and freeness properties of the generic Hopf Galois extensions

Christian Kassel, Akira Masuoka

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