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Nuclear dimension and classification of $ \mathrm{C}^*$-algebras associated to Smale spaces


Authors: Robin J. Deeley and Karen R. Strung
Journal: Trans. Amer. Math. Soc. 370 (2018), 3467-3485
MSC (2010): Primary 46L35, 37D20
DOI: https://doi.org/10.1090/tran/7046
Published electronically: December 18, 2017
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Abstract: We show that the homoclinic $ \mathrm {C}^*$-algebras of mixing Smale spaces are classifiable by the Elliott invariant. To obtain this result, we prove that the stable, unstable, and homoclinic $ \mathrm {C}^*$-algebras associated to such Smale spaces have finite nuclear dimension. Our proof of finite nuclear dimension relies on Guentner, Willett, and Yu's notion of dynamic asymptotic dimension.


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Additional Information

Robin J. Deeley
Affiliation: Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, Keller 401A, Honolulu, Hawaii 96822
Email: robin.deeley@gmail.com

Karen R. Strung
Affiliation: Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-656 Warszawa, Poland
Email: kstrung@math.ru.nl

DOI: https://doi.org/10.1090/tran/7046
Keywords: Smale spaces, classification of nuclear $\mathrm{C}^{*}$-algebras, nuclear dimension
Received by editor(s): January 19, 2016
Received by editor(s) in revised form: August 10, 2016
Published electronically: December 18, 2017
Additional Notes: The second listed author was supported by an IMPACT fellowship cofunded by Ministry of Science and Higher Education grant 3038/7.PR/2014/2 and EC grant PCOFUND-GA-2012-600415, and the Sonata 9 NCN grant 2015/17/D/ST1/02529
Article copyright: © Copyright 2017 American Mathematical Society

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