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Transactions of the American Mathematical Society Series B

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Strong classification of purely infinite Cuntz-Krieger algebras


Authors: Toke Meier Carlsen, Gunnar Restorff and Efren Ruiz
Journal: Trans. Amer. Math. Soc. Ser. B 4 (2017), 1-30
MSC (2010): Primary 46L35, 46L80; Secondary 46L55, 37B10
DOI: https://doi.org/10.1090/btran/14
Published electronically: March 17, 2017
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Abstract: In 2006, Restorff completed the classification of all Cuntz-Krieger algebras with finitely many ideals (i.e., those that are purely infinite) up to stable isomorphism. He left open the questions concerning strong classification up to stable isomorphism and unital classification. In this paper, we address both questions. We show that any isomorphism between the reduced filtered $ K$-theory of two Cuntz-Krieger algebras with finitely many ideals lifts to a $ ^*$-isomorphism between the stabilized Cuntz-Krieger algebras. As a result, we also obtain strong unital classification.


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Additional Information

Toke Meier Carlsen
Affiliation: Department of Science and Technology, University of the Faroe Islands, Nóatún 3, FO-100 Tórshavn, the Faroe Islands
Email: tokemc@setur.fo

Gunnar Restorff
Affiliation: Department of Science and Technology, University of the Faroe Islands, Nóatún 3, FO-100 Tórshavn, the Faroe Islands
Email: gunnarr@setur.fo

Efren Ruiz
Affiliation: Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii 96720-4091
Email: ruize@hawaii.edu

DOI: https://doi.org/10.1090/btran/14
Keywords: Cuntz-Krieger algebras, graph $C^*$-algebras, $K$-theory, flow equivalence
Received by editor(s): June 21, 2016
Received by editor(s) in revised form: October 28, 2016
Published electronically: March 17, 2017
Article copyright: © Copyright 2017 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)