Hom-Novikov color algebras

TL;DR

This paper introduces Hom-Novikov color algebras, explores their constructions, properties, and related structures, and demonstrates their connections to Hom-Lie color algebras, expanding the algebraic framework.

Contribution

It presents the first systematic study of Hom-Novikov color algebras, including their constructions, properties, and relations to other algebraic structures.

Findings

Hom-Novikov color algebras can be constructed from existing ones using morphisms.

Any Hom-Novikov color algebra is Hom-Lie admissible.

Hom-quadratic Hom-Novikov color algebras have specific twisting properties.

Abstract

The aim of this paper is to introduce Hom-Novikov color algebras and give some constructions of Hom-Novikov color algebras from a given one and a (weak) morphism. Other interesting constructions using averaging operators, centroids, derivations and tensor product are given. We also proved that any Hom-Novikov color algebra is Hom-Lie admissible. Moreover, we introduce Hom-quadratic Hom-Novikov color algebras and provide some properties by twisting. It is also shown that the Hom-Lie color algebra associated to a given quadratic Hom-Novikov color algebra is also quadratic.