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

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- by Andrew S. Toms PDF
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**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.## References

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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