  In this article we prove that there exists a Dixmier map for nilpotent super
Lie algebras. In other words, if we denote by Prim(U(g)) the set of (graded)
primitive ideals of the enveloping algebra U(g) of g and Ad_0 the adjoint group
of g_0, we prove that the usual Dixmier map for nilpotent Lie algebras can be
naturally extended to the context of nilpotent super Lie algebras, i.e. there
exists a bijective map \[ I : g_0^*/Ad_0 \rightarrow Prim(U(g)), \] defined by
sending the equivalence class [lambda] of a functional lambda to a primitive
ideal I(lambda) of U(g), and which coincides with the Dixmier map in the case
of nilpotent Lie algebras. Moreover, the construction of the previous map is
explicit, and more or less parallel to the one for Lie algebras, a major
difference with a previous approach. One key fact in the construction is the
existence of polarizations for super Lie algebras, generalizing the concept
defined for Lie algebras. As a corollary of the previous description, we obtain
that the quotient of the enveloping algebra by the ideal I(lambda) is
isomorphic to the tensor product Cliff_q(k) \otimes A_p(k) of a Clifford
algebra and a Weyl algebra, where (p,q) =
(dim(g_0/g_0^{lambda})/2,dim(g_1/g_1^{lambda})), we get a direct construction
of the maximal ideals of the underlying algebra of U(g) and also some
properties of the stabilizers of the primitive ideals of U(g).
