Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a
cohomological characterization of Leibniz central extensions of Lie algebras is
given based on Corollary 3.3 and Theorem 3.5. In particular, as applications,
we obtain the cohomological version of Gao's main Theorem in \cite{Gao2} for
Kac-Moody algebras and answer a question in \cite{LH}.Comment: 12 pages. Proc. Amer.Math.Soc. (to appear in a simplified version