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An infinite family of non-isomorphic C$ ^*$-algebras with identical $ \mathrm{K}$-theory


Author: Andrew S. Toms
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
Published electronically: May 21, 2008
MathSciNet review: 2415076
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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

DOI: https://doi.org/10.1090/S0002-9947-08-04583-2
Received by editor(s): September 15, 2006
Published electronically: May 21, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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