Minimal Primal and Glimm Ideal Spaces of Group C*-Algebras

Abstract Due to recent work of Archbold and others primal and Glimm ideals in C *-algebras have gained considerable attention. They turned out to be important in representing a C *-algebra as a maximal full algebra of cross sections and in the estimation of norms of inner derivations. In this paper we determine the topological spaces of minimal primal and of Glimm ideals in group C *-algebras for several classes of locally compact groups, including all amenable discrete groups, the classical motion groups, and certain semi-direct products of vector groups with the reals.