Induced characters, Mackey analysis and primitive ideal spaces of nilpotent discrete groups

Let G be a nilpotent discrete group and Prim(C∗(G)) the primitive ideal space of the group C∗-algebra C∗(G). If G is either finitely generated or has absolutely idempotent characters, we are able to describe the hull-kernel topology on Prim(C∗(G)) in terms of a topology on a parametrizing space of subgroupcharacter pairs. For that purpose, we introduce and study induced traces and develop a Mackey machine for characters. We heavily exploit the fact that the groups under consideration have the property that every faithful character vanishes outside the finite conjugacy class subgroup. © 2006 Elsevier Inc. All rights reserved.