An infinite family of non-isomorphic C*-algebras with identical 𝐾-theory

Toms, Andrew

doi:10.1090/S0002-9947-08-04583-2

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