Abstract
The aim of this paper is to study bialgebras(Hopf algebras) on the skew polynomial algebras $$R[z;\sigma ]$$ 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 $$R[z;\sigma ]$$ and on the quotients of $$R[z;\sigma ]/I$$, for a certain Hopf ideal I of $$R[z;\sigma ]$$. 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.
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