Characterization of Automorphisms of ( θ, ω )-Twisted Radford’s Hom-Biproduct

Xing Wang and Ding-Guo Wang
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Xing Wang: Department of Mathematics, Jining University, Qufu 273155, China
Ding-Guo Wang: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2022, vol. 10, issue 3, 1-20

Abstract: In this paper, we study the Hom–Hopf algebra automorphism group of a ( θ , ω ) -twisted-Radford’s Hom-biproduct, which satisfies certain conditions. First, we study the endomorphism monoid and automorphism group of ( θ , ω ) -twisted Radford’s Hom-biproducts, and show that the endomorphism has a factorization closely related to the factors ( A , α ) and ( H , β ) . Then, we consider ( θ , ω ) -twisted Radford’s Hom-biproduct automorphism group Aut Hom - Hopf ( A × ω θ H , p ) as a subgroup of some semidirect product U ( C , A ) op ⋊ φ G ( A ) . Finally, we characterize the automorphisms of a concrete example.

Keywords: Hom–Hopf algebra; twisted Radford’s Hom-biproduct; automorphism (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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