Ore Extensions for the Sweedler’s Hopf Algebra H 4

Shilin Yang and Yongfeng Zhang
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Shilin Yang: School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China
Yongfeng Zhang: School of Mathematics, Faculty of Science, Beijing University of Technology, Beijing 100124, China

Mathematics, 2020, vol. 8, issue 8, 1-24

Abstract: The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H 4 [ z ; σ ] of automorphism type for the Sweedler ′ s 4-dimensional Hopf algebra H 4 . Firstly, we calculate all equivalent classes of twisted homomorphisms ( σ , J ) for H 4 . Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H 4 [ z ; σ ] up to isomorphism.

Keywords: Ore extension; Drinfeld twist; twisted homomorphism; Hopf algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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