Stable rank of the reduced $C^*$-algebras of non-amenable Lie groups of type I

Abstract

In this paper we show that stable rank of the reduced C * -algebras of connected non-compact real semi-simple Lie groups is estimated by real rank of these groups. We extend this result to the case of connected reductive Lie groups and partially even to the case of connected non-amenable real Lie groups of type I. As a corollary, we show that the product formula of stable rank holds for locally compact, -compact non-amenable groups of type I.