On abelian extensions of color Lie algebras by their modules

Given a color Lie algebra [Formula: see text] and an [Formula: see text]-module [Formula: see text], we obtain a color Lie algebra [Formula: see text] which is a subalgebra of the derivation algebra of the semidirect sum [Formula: see text]. By using a representation of [Formula: see text] on the second cohomology group [Formula: see text] we obtain the Wells mapping, which is shown to be applicable to measure extensibility of pairs of derivations. We use [Formula: see text], [Formula: see text] and the Wells mapping to deduce the Wells sequence for any abelian extension of [Formula: see text] by [Formula: see text].