Extensões H-cleft distinguidas por H-identidades polinomiais

Abstract

Our main object of study is the well-known question asking whether the set of polynomials identities distinguishes PI-algebras up to isomorphism. Let k be an algebraically closed field of characteristic 0 and H a non-semisimple monomial Hopf algebra. We prove that H-Galois objects over k are determined up to H-comodule algebra isomorphism by their polynomial H-identities. Afterwards we show that if H_N^q is a Taft algebra over a finite commutative unital ring R and N is an invertible element in R, then the H_N^q-cleft extensions over R are determined up to H_N^q-comodule R-algebra isomorphism by their polynomial H_N^q-identities.