Enveloping algebras for Hom-Lie algebras in Hom-Yetter—Drinfeld categories

In this paper, we first introduce the definition of braided Hom-Lie algebras and present some construction methods. Second, we study the central invariant theory for braided Hom-Lie algebras and prove that the enveloping algebras of braided Hom-Lie algebras are $H$-cocommutative Hom-Hopf algebras. Finally, we study Radford's Hom-biproduct, and therefore obtain the Schur—Weyl duality in the setting of Hom-Hopf algebras.