Hom-Lie color algebra structures

TL;DR

This paper introduces Hom-Lie color algebras as a broad generalization of existing algebraic structures, explores their homomorphisms, constructs new examples via twists, and classifies related admissible algebras.

Contribution

It defines Hom-Lie color algebras, studies their homomorphisms, constructs new algebras through -twists, and classifies admissible algebras using G-Hom-associative color algebra frameworks.

Findings

Hom-Lie color algebras generalize Lie (super) and Lie color algebras.

Construction of new algebras via -twists.

Classification of admissible algebras using G-Hom-associative structures.

Abstract

This paper introduces the notion of Hom-Lie color algebra, which is a natural general- ization of Hom-Lie (super)algebras. Hom-Lie color algebras include also as special cases Lie (super) algebras and Lie color algebras. We study the homomorphism relation of Hom-Lie color algebras, and construct new algebras of such kind by a \sigma-twist. Hom-Lie color admissible algebras are also defined and investigated. They are finally classified via G-Hom-associative color algebras, where G is a subgroup of the symmetric group S_3.