  Let M be a 1-motive defined over a field of characteristic 0. To M we can
associate its motivic Galois group, G_mot(M), which is the geometrical
interpretation of the Munford-Tate group of M. We prove that the unipotent
radical of the Lie algebra of G_mot(M) is the semi-abelian variety defined by
the adjoint action of the semi-simplified of the Lie algebra of G_mot(M) on
itself.
