Dimension theory of group \(C^*\)-algebras of connected Lie groups of type I. (English) Zbl 0971.46039

Sudo, Takahiro

J. Math. Soc. Japan 52, No. 3, 583-590 (2000).

Summary: 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.

MSC:

46L05	General theory of \(C^*\)-algebras
22D25	\(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
46L80	\(K\)-theory and operator algebras (including cyclic theory)

Keywords:

isomorphism classes of connected solvable Lie groups; group \(C^*\)-algebras; stable rank; closed normal subgroups and quotient groups