Normalization of a nonlinear representation of a Lie algebra, regular on an abelian ideal

We consider a nonlinear representation of a Lie algebra which is regular on an abelian ideal, we define a normal form which generalizes that defined in [D. Arnal, M. Ben Ammar, M. Selmi, {\rm Normalisation d'une repr\'esentation non lin\'eaire d'une alg\`ebre de Lie}. {\it Annales de la Facult\'e des Sciences de Toulouse}, 5e s\'erie, tome 9, No 3, 1988, p 355--379.]