Flatness and freeness properties of the generic Hopf Galois extensions

• Autores: Christian Kassel, Akira Masuoka
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 51, Nº. 1, 2010, págs. 79-94
• Idioma: inglés
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• Resumen

  • 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.