Stable Rank of $C^*$-Algebras of Continuous Fields

Abstract

The $C^*$-algebras of continuous fields are enlarged and embedded into the associated direct products, and their stable rank and connected stable rank are estimated in terms of their base spaces and fibers. Using these estimates, we compute these ranks of $C^*$-algebras of continuous fields of elementary $C^*$-algebras, and those of group $C^*$-algebras of the discrete Heisenberg groups.