JournalsprimsVol. 39 , No. 2DOI 10.2977/prims/1145476102

The Structure of Group <em>C</em><sup>∗</sup>-algebras of the Generalized Dixmier Groups

  • Takahiro Sudo

    Ryukyu University, Okinawa, Japan
The Structure of Group <em>C</em><sup>∗</sup>-algebras of the Generalized Dixmier Groups cover

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.