Dimension theory of group C^*-algebras of connected Lie groups of type I

Abstract

In this paper we determine isomorphism classes of connected solvable Lie groups with some conditions such that their group C^*-algebras have stable rank one, and give its applications. Also, we show that stable rank of group C^*-algebras of connected Lie groups of type I is estimated in terms of their closed normal subgroups and quotient groups.