Structure of group $C^*$-algebras of the generalized Mautner groups

Abstract

We construct finite composition series of group $C^{*}$-algebras of the generalized Mautner groups whose subquotients are tensor products of commutative $C^{*}$-algebras, noncommutative tori and the $C^{*}$-algebra of compact operators. As an application, we estimate the stable rank and connected stable rank of the $C^{*}$-algebras of generalized real Mautner groups.