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One-parameter continuous fields of Kirchberg algebras with rational $ K$-theory


Authors: Rasmus Bentmann and Marius Dadarlat
Journal: Proc. Amer. Math. Soc. 143 (2015), 3455-3463
MSC (2010): Primary 46L35, 46L80, 19K35, 46M20
DOI: https://doi.org/10.1090/proc12742
Published electronically: April 16, 2015
MathSciNet review: 3348788
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Abstract: We show that separable continuous fields over the unit interval whose fibers are stable Kirchberg algebras that satisfy the universal coefficient theorem in $ \textup {KK}$-theory (UCT) and have rational $ \textup {K}$-theory groups are classified up to isomorphism by filtrated $ \textup {K}$-theory.


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Additional Information

Rasmus Bentmann
Affiliation: Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3–5, 37073 Göttingen, Germany
Email: rbentma@uni-math.gwdg.de

Marius Dadarlat
Affiliation: Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, Indiana 47907-2067
Email: mdd@math.purdue.edu

DOI: https://doi.org/10.1090/proc12742
Keywords: Kirchberg algebras, continuous fields, $K$-theory
Received by editor(s): November 4, 2013
Published electronically: April 16, 2015
Additional Notes: The first author was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and by the Marie Curie Research Training Network EU-NCG
The second author was partially supported by NSF grant #DMS–1101305
Communicated by: Marius Junge
Article copyright: © Copyright 2015 American Mathematical Society

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