Ranks and embeddings of C^*-algebras of continuous fields
by
Takahiro Sudo
University of the Ryukyus

In this talk we estimate the stable rank, connected stable rank and real rank of C*-algebras of continuous fields on locally compact Hausdorff spaces in terms of their base spaces and fibers. The key idea of this main result is to enlarge continuous fields to embed into the direct sums associated with base spaces and fibers. Using these rank estimations, we compute the ranks of group C*-algebras of the generalized, discrete Heisenberg groups and Heisenberg Lie groups, and estimate the ranks of C*-algebras of continuous fields of elementary C*-algebras. Moreover, we show that these C*-algebras are embeddable into the inductive limits arising from their associated direct sums.

Date received: May 30, 2000