Representations and $T^{\ast}$-extensions of $\delta$-Bihom-Jordan-Lie algebras

Abstract

The purpose of this article is to study representations of $\delta$-Bihom-Jordan-Lie algebras. In particular, adjoint representations, trivial representations, deformations, $T^\ast$-extensions of $\delta$-Bihom-Jordan-Lie algebras are studied in detail. Derivations and central extensions of $\delta$-Bihom-Jordan-Lie algebras are also discussed as an application.