Álgebras de Hopf, objetos galois e identidades polinomiais

Abstract

Our main goal is to study Hopf algebras and Galois objects, from the point of view of the polynomial identities, more precisely how these objects are distinguished by their polynomial H-identities. To this end we follow the program started by C. Kassel. There he defines polynomial H-identities to H-comodule algebras, gives some properties of these T-ideals and uses Galois objects classifications, as made by Bichon for the monomial Hopf algebras of type I, to find polynomial identities that distinguish those objects. In that case, the existence of an algebra homomorphism such that the kernel coincides with the T-ideal of the H-identities is crucial.