The Structure of Group C^*-algebras of the Generalized Dixmier Groups

Abstract

In this paper we first analyze the algebraic structure of group C^*-algebras of the generalized Dixmier groups, and next consider that of group C^*-algebras of some Lie semi-direct products with multi-diagonal or diagonal actions. As an application, we estimate the stable rank and the connected stable rank of these C^*-algebras in terms of groups. Also, we show that some of these group C^*-algebras have no nontrivial projections.