Representations and $T$*-extensions of hom-Jordan-Lie algebras

TL;DR

This paper investigates the structure and properties of hom-Jordan-Lie algebras, focusing on their representations, extensions, and derivations, providing new insights into their algebraic behavior.

Contribution

It introduces and analyzes $T$*-extensions and various representations of hom-Jordan-Lie algebras, expanding understanding of their algebraic structure and applications.

Findings

Detailed study of adjoint and trivial representations

Characterization of $T$*-extensions and their properties

Analysis of derivations and central extensions

Abstract

The purpose of this paper is to study representations and $T$*-extensions of hom-Jordan-Lie algebras. In particular, adjoint representations, trivial representations, deformations and many properties of $T$*-extensions of hom-Jordan-Lie algebras are studied in detail. Derivations and central extensions of hom-Jordan-Lie algebras are also discussed as an application.