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

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)
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