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

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.