The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
We investigate the structure of the \(C^ *\)-algebras associated with minimal homeomorphisms of the Cantor set via the crossed product construction. The \(C^ *\)-algebras exhibit many of the same properties as approximately finite dimensional (or AF) \(C^ *\)-algebras. Specifically, each non-empty closed subset 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 \(K_ 0\)-groups. We examine examples arising from the theory of interval exchange transformations.
\(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set via the crossed product construction
approximately finite dimensional \(C^*\)-algebras
scientific article; zbMATH DE number 4026153