## Circle Maps and C*-algebras

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### Standard

Circle Maps and C*-algebras. / Schmidt, Thomas Lundsgaard; Thomsen, Klaus.

I: Ergodic Theory and Dynamical Systems, Bind 35, Nr. 2, 2015, s. 546-584.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

### Harvard

Schmidt, TL & Thomsen, K 2015, 'Circle Maps and C*-algebras', Ergodic Theory and Dynamical Systems, bind 35, nr. 2, s. 546-584. https://doi.org/10.1017/etds.2013.64

### APA

Schmidt, T. L., & Thomsen, K. (2015). Circle Maps and C*-algebras. Ergodic Theory and Dynamical Systems, 35(2), 546-584. https://doi.org/10.1017/etds.2013.64

### CBE

Schmidt TL, Thomsen K. 2015. Circle Maps and C*-algebras. Ergodic Theory and Dynamical Systems. 35(2):546-584. https://doi.org/10.1017/etds.2013.64

### MLA

Schmidt, Thomas Lundsgaard og Klaus Thomsen. "Circle Maps and C*-algebras". Ergodic Theory and Dynamical Systems. 2015, 35(2). 546-584. https://doi.org/10.1017/etds.2013.64

### Vancouver

Schmidt TL, Thomsen K. Circle Maps and C*-algebras. Ergodic Theory and Dynamical Systems. 2015;35(2):546-584. https://doi.org/10.1017/etds.2013.64

### Author

Schmidt, Thomas Lundsgaard ; Thomsen, Klaus. / Circle Maps and C*-algebras. I: Ergodic Theory and Dynamical Systems. 2015 ; Bind 35, Nr. 2. s. 546-584.

### Bibtex

@article{6e155af165f74386b675e8907171b25d,
title = "Circle Maps and C*-algebras",
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. ",
author = "Schmidt, {Thomas Lundsgaard} and Klaus Thomsen",
year = "2015",
doi = "10.1017/etds.2013.64",
language = "English",
volume = "35",
pages = "546--584",
journal = "Ergodic Theory and Dynamical Systems",
issn = "0143-3857",
publisher = "Cambridge University Press",
number = "2",

}

### RIS

TY - JOUR

T1 - Circle Maps and C*-algebras

AU - Schmidt, Thomas Lundsgaard

AU - Thomsen, Klaus

PY - 2015

Y1 - 2015

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

VL - 35

SP - 546

EP - 584

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 2

ER -