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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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An infinite family of non-isomorphic C$^*$-algebras with identical $\mathrm {K}$-theory
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by Andrew S. Toms PDF
Trans. Amer. Math. Soc. 360 (2008), 5343-5354 Request permission

Abstract:

We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C$^*$-algebras which agree on $\mathrm {K}$-theory and traces. The algebras do not absorb the Jiang-Su algebra $\mathcal {Z}$ tensorially, answering a question of N. C. Phillips. They are also pairwise shape and Morita equivalent, confirming a conjecture from our earlier work. The distinguishing invariant is the radius of comparison, a non-stable invariant of the Cuntz semigroup.
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Additional Information
  • Andrew S. Toms
  • Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele St.,Toronto, Ontario, Canada M3J 1P3
  • Email: atoms@mathstat.yorku.ca
  • Received by editor(s): September 15, 2006
  • Published electronically: May 21, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 5343-5354
  • MSC (2000): Primary 46L35; Secondary 46L80
  • DOI: https://doi.org/10.1090/S0002-9947-08-04583-2
  • MathSciNet review: 2415076