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

Abstract

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 subgroup-character 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.