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Do Phantom Cuntz-Krieger Algebras Exist?

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Operator Algebra and Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 58))

Abstract

If phantom Cuntz-Krieger algebras do not exist, then purely infinite Cuntz-Krieger algebras can be characterized by outer properties. In this survey paper, a summary of the known results on non-existence of phantom Cuntz-Krieger algebras is given.

Mathematics Subject Classification (2010): 46L55, 46L35, 46L80, 46M15.

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Acknowledgements

This research was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92), and by the NordForsk Research Network “Operator Algebra and Dynamics” (grant #11580).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

    Sara E. Arklint

Authors
  1. Sara E. Arklint
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Correspondence to Sara E. Arklint .

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Editors and Affiliations

  1. Dept. of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Toke M. Carlsen

  2. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Søren Eilers

  3. Dept. of Science and Technology, University of the Faroe Islands, Tórshavn, Faroe Islands

    Gunnar Restorff

  4. Culture and Communication (UKK) Division of Applied Mathematics The School of Education, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

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Arklint, S.E. (2013). Do Phantom Cuntz-Krieger Algebras Exist?. In: Carlsen, T., Eilers, S., Restorff, G., Silvestrov, S. (eds) Operator Algebra and Dynamics. Springer Proceedings in Mathematics & Statistics, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39459-1_2

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