On the centre of crossed modules of Lie algebras

This paper studies the relationship between crossed modules of Lie algebras and their centres. We show that any crossed module $\mathrm{\partial }:L_1\to L_0$ of Lie algebras fits in an exact sequence involving cohomology of the homotopy Lie algebras ${\pi }_0(L_{\ast })$ and ${\pi }_1(L_{\ast })$.