Article contents
Circle maps and
${C}^{\ast } $-algebras
Published online by Cambridge University Press: 28 August 2013
Abstract
We consider a construction of ${C}^{\ast } $-algebras from continuous piecewise monotone maps on the circle which generalizes the crossed product construction for homeomorphisms and more generally the construction of Renault, Deaconu and Anantharaman-Delaroche for local homeomorphisms. Assuming that the map is surjective and not locally injective we give necessary and sufficient conditions for the simplicity of the
${C}^{\ast } $-algebra and show that it is then a Kirchberg algebra. We provide tools for the calculation of the
$K$-theory groups and turn them into an algorithmic method for Markov maps.
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- Research Article
- Information
- Copyright
- © Cambridge University Press, 2013
References
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