STABLE RANK OF THE C*-ALGEBRAS OF NILPOTENT LIE GROUPS

Abstract

The stable rank of the C*-algebras of simply connected nilpotent Lie groups is determined by the dimension of the fixed point subspaces of the real adjoint spaces of the Lie algebras under the coadjoint actions, which is a generalization of the result obtained by A. J-L. Sheu. This equality is no longer affirmative in the case of non-nilpotent Lie groups.