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.
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Takahiro Sudo, The Structure of Group <em>C</em><sup>∗</sup>-algebras of the Generalized Dixmier Groups. Publ. Res. Inst. Math. Sci. 39 (2003), no. 2, pp. 205–225DOI 10.2977/PRIMS/1145476102