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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Nuclear dimension and classification of $\mathrm {C}^*$-algebras associated to Smale spaces
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by Robin J. Deeley and Karen R. Strung PDF
Trans. Amer. Math. Soc. 370 (2018), 3467-3485 Request permission

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
  • MR Author ID: 741108
  • Email: robin.deeley@gmail.com
  • Karen R. Strung
  • Affiliation: Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-656 Warszawa, Poland
  • MR Author ID: 924942
  • Email: kstrung@math.ru.nl
  • 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
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3467-3485
  • MSC (2010): Primary 46L35, 37D20
  • DOI: https://doi.org/10.1090/tran/7046
  • MathSciNet review: 3766855