We investigate the structure
of the C∗-algebras associated with minimal homeomorphisms of the Cantor set via
the crossed product construction. These C∗-algebras exhibit many of the same
properties as approximately finite dimensional (or AF) C∗-algebras. Specifically, each
non-empty closed subset of the Cantor set is shown to give rise, in a natural way, to
an AF-subalgebra of the crossed product and we analyze these subalgebras. Results
of Versik show that the crossed product may be embedded into an AF-algebra.
We show that this embedding induces an order isomorphism at the level of
K0-groups. We examine examples arising from the theory of interval exchange
transformations.
