Two Order Jacobi-Courant Algebra

In this paper, the problem that the Lie algebra which is still a Lie algebra through twice abelian extension of Leibniz algebra is proposed based on the previous studies. Firstly, according to the definition of the abelian extension of Leibniz algebra, we can obtain that the abelian extension of Lie algebra by is still a Lie algebra. And then we obtain the extension of Lie algebra and define a bracket on the extension. Moreover we can prove that the abelian extension of Leibniz algebra is still a Lie algebra.