Drinfeld Codoubles of Hom–Hopf Algebras

Abstract

The main purpose of the present paper is to develop the theory of center constructions on Hom–Hopf algebras. Let H be a Hom–Hopf algebra, we first introduce the notions of nth Yetter–Drinfeld modules and mth Drinfeld codouble for H. Also we prove that the category $${\mathcal {YD}}_H^H(n)$$ of nth Yetter–Drinfeld modules of H is a braided autonomous category. Finally, we show that $${\mathcal {YD}}_H^H(n)$$ and $$Corep^{i,j}(CD_m(H))$$ (i.e., the corepresentation category of the Drinfeld codouble of H) are braided isomorphic as the full subcategories of $$Corep^{i,j}(H)$$ .