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

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 AutHom-Hopf(A×ωθH,p) as a subgroup of some semidirect product U(C,A)op⋊φG(A). Finally, we characterize the automorphisms of a concrete example.