Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman Color Hom-Algebras

The main feature of color Hom-algebras is that the identities defining the structures are twisted by even linear maps. The purpose of this paper is to introduce and give some constructions of admissible Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras. Their bimodules and matched pairs are defined and the relevant properties and theorems are given. Also, the connections between Hom-Novikov-Poisson color Hom-algebras and Hom-Gelfand-Dorfman color Hom-algebras are proved. Furthermore, we show that the class of admissible Hom-Novikov-Poisson color Hom-algebras is closed under tensor product.