Abstract
The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H4[z;σ] of automorphism type for the Sweedler′s 4-dimensional Hopf algebra H4. Firstly, we calculate all equivalent classes of twisted homomorphisms (σ,J) for H4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H4[z;σ] up to isomorphism.
Highlights
Ore extensions play a key role in classifying pointed Hopf algebras, see for example [1,2,3,4,5]
Panov [7] introduced the concept of Hopf-Ore extension R[ x; σ, δ] of which the variable x is restricted to a skew primitive element and gave some equivalent descriptions
The authors [12] gave the realization of PBW-deformations of an quantum group via iterated Ore extensions
Summary
Ore extensions play a key role in classifying pointed Hopf algebras, see for example [1,2,3,4,5]. We study Ore extensions of automorphism type for the Hopf algebra H4. One fundamental result (Theorem 1) about the Ore extensions of automorphism type for Hopf algebras is established. Mathematics 2020, 8, 1293 algebras structures on the quotients of Ore extensions of automorphism type for H4 are classified (Theorem 4)
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