Representations of hom-Lie algebras

TL;DR

This paper explores the structure and representations of hom-Lie algebras, focusing on their adjoint and trivial representations, and investigates derivations, deformations, and extensions as applications.

Contribution

It provides a detailed analysis of representations of hom-Lie algebras and examines their derivations, deformations, and extensions, advancing understanding of their algebraic properties.

Findings

Detailed study of adjoint and trivial representations

Analysis of derivations and deformations of hom-Lie algebras

Insights into central and derivation extensions

Abstract

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.