On the centre of crossed modules of Lie algebras

Abstract

This paper studies the relationship between crossed modules of Lie algebras and their centres. We show that any crossed module \(\partial : L_1\to L_0\) of Lie algebras fits in an exact sequence involving cohomology of the homotopy Lie algebras \(π_0(L_*)\) and \(π_1(L_*)\).

arXiv admin note: substantial text overlap with arXiv:2109.00981