On the topological stable rank of certain transformation group \(C^*\)- algebras. (English) Zbl 0667.46045

Putnam, Ian F.

Ergodic Theory Dyn. Syst. 10, No. 1, 197-207 (1990).

We consider the crossed product or transformation group \(C^*\)-algebras arising from actions of the group of integers on a totally disconnected compact metrizable space. Under a mild hypothesis, we give a necessary and sufficient dynamical condition for the invertibles in such a \(C^*\)- algebra to be dense. We also examine the property of residual finiteness for such \(C^*\)-algebras.

Reviewer: I.F.Putnam

MSC:

46L55

Noncommutative dynamical systems

Keywords:

topological stable rank; transformation group \(C^*\)-algebras; crossed product or transformation group \(C^*\)-algebras arising from actions of the group of integers on a totally disconnected compact metrizable space; necessary and sufficient dynamical condition for the invertibles in such a \(C^*\)-algebra to be dense; residual finiteness

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