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

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.