The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
type: Item
instance of: scholarly article
title: The \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set
zbMATH Open document ID: 0631.46068
author: Ian F. Putnam
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L80
zbMATH DE Number: 4026153
zbMATH Keywords: \(C^*\)-algebras associated with minimal homeomorphisms of the Cantor set via the crossed product construction
zbMATH Keywords: approximately finite dimensional \(C^*\)-algebras
zbMATH Keywords: AF-subalgebra
zbMATH Keywords: \(K_ 0\)-groups
zbMATH Keywords: interval exchange transformations
MaRDI profile type: Publication
full work available at URL: pjm.1989.136.329
OpenAlex ID: W2062803982
DOI: 10.2140/PJM.1989.136.329
description: scientific article; zbMATH DE number 4026153