The Factorization for a Class of Hom-Coalgebras

Abstract

Let ( , ) be a Hom-Hopf algebra and ( , ) a Hom-coalgebra. In this paper, we first introduce the notions of Hom-crossed coproduct ⋊ and cleft coextension and then discuss the equivalence between them. Furthermore, we discuss the relation between cleft coextension and Hom-module coalgebra with the Hom-Hopf module structure and obtain a Hom-coalgebra factorization for Hom-module coalgebra with the Hom-Hopf module structure.

Some Results About Hom-Comodule Algebras With Hom-Hopf Module Structure

“…On the other hand, we have obtained the coalgebra factorization of right H-Hom-module coalgebras with Hom-Hopf module structure (see [3], Theorem 4.1). given by…”