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

摘要

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.