Characters and Primitive Ideal Spaces of Nilpotent Discrete Groups

If G is a discrete abelian group, then the space of maximal ideals of the L¹- and the C*-algebra of G is homeomorphic to the compact dual group of G. This generalizes to some extent to discrete nilpotent groups G, where the the dual group has to be replaced by the space of characters of G and the main problem is the description of the hull-kernel topology on the primitive ideal space in terms of a topology on the space of characters. Very satisfying results have been obtained for finitely generated nilpotent groups.