Ore Extensions of Automorphism Type for Hopf Algebras

The aim of this paper is to study bialgebras(Hopf algebras) on the skew polynomial algebras R[ z; s] of automorphism type, which comultiplication defined on the variable z is extended by a Drinfeld twist J for a Hopf algebra R. Firstly, we establish some necessary and sufficient conditions that are of Hopf algebra structures on the localization of skew polynomial ring R[z; s] and on the quotients of R[ z; s]/I, for a certain Hopf ideal I of R[ z; s]. Then, we give some examples for these results. Specially, the non-semisimple and non-pointed 16 dimension self-dual Hopf algebra is also constructed by the Ore extensions of automorphism type.