On stably finiteness for $C^{\ast }$-algebras of exponential solvable Lie groups

Abstract

We study the link between stably finiteness and stably projectionless-ness for $C^{\ast }$-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by $4$; otherwise, they are not necessarily equivalent. To provide examples proving the last assertion, we study exponential solvable Lie groups that have nonempty finite open sets in their unitary dual.

35 pages

References in corpus (2)

• Structure and applications of real C*-algebras
• AF-embeddability for Lie groups with $T_1$ primitive ideal spaces

Cited by in corpus (1)

• Square-integrable representations and the coadjoint action of solvable Lie groups