Circle Maps and C*-algebras

Thomas Lundsgaard Schmidt; Klaus Thomsen

doi:10.1017/etds.2013.64

Circle Maps and C*-algebras

Thomas Lundsgaard Schmidt, Klaus Thomsen

Department of Mathematics

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1 Citation (Scopus)

Abstract

We consider a construction of $C^*$-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 $C^*$-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.

Translated title of the contribution	Cirkelafbildninger og C*-algebraer
Original language	English
Journal	Ergodic Theory and Dynamical Systems
Volume	35
Issue	2
Pages (from-to)	546-584
Number of pages	39
ISSN	0143-3857
DOIs	https://doi.org/10.1017/etds.2013.64
Publication status	Published - 2015

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10.1017/etds.2013.64

Cite this

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abstract = "We consider a construction of $C^*$-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 $C^*$-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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AU - Thomsen, Klaus

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N2 - We consider a construction of $C^*$-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 $C^*$-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.

AB - We consider a construction of $C^*$-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 $C^*$-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.

U2 - 10.1017/etds.2013.64

DO - 10.1017/etds.2013.64

M3 - Journal article

SN - 0143-3857

VL - 35

SP - 546

EP - 584

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 2

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