Admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras

TL;DR

This paper introduces and constructs new classes of color Hom-algebras twisted by linear maps, explores their bimodules and matched pairs, and establishes their structural properties and interrelations.

Contribution

It presents the first definitions and constructions of admissible Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras, including their bimodules, matched pairs, and tensor product closure.

Findings

Defined bimodules and matched pairs for these algebras

Proved the connection between Hom-Novikov-Poisson and Hom-Gelfand-Dorfman color Hom-algebras

Showed closure under tensor product for admissible Hom-Novikov-Poisson color Hom-algebras

Abstract

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 is proved. Furthermore, we show that the class of admissible Hom-Novikov-Poisson color Hom-algebras is closed under tensor product.