On crossed modules of pre-Lie algebras

Given a Lie algebra [Formula: see text] and a [Formula: see text]-module [Formula: see text], it is due to Gerstenhaber that there is an isomorphism between [Formula: see text] and the group of equivalence classes of crossed modules with kernel [Formula: see text] and cokernel [Formula: see text]. The goal of this paper is to obtain this result for pre-Lie algebras and their modules.