Strong classification of purely infinite Cuntz-Krieger algebras
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- by Toke Meier Carlsen, Gunnar Restorff and Efren Ruiz HTML | PDF
- Trans. Amer. Math. Soc. Ser. B 4 (2017), 1-30
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.References
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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
- MR Author ID: 685180
- ORCID: 0000-0002-7981-7130
- 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
- MR Author ID: 799161
- Email: gunnarr@setur.fo
- Efren Ruiz
- Affiliation: Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii 96720-4091
- MR Author ID: 817213
- Email: ruize@hawaii.edu
- Received by editor(s): June 21, 2016
- Received by editor(s) in revised form: October 28, 2016
- Published electronically: March 17, 2017
- © Copyright 2017 by the authors under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- 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
- MathSciNet review: 3624419