Z-stable ASH algebras

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The Jiang--Su algebra Z has come to prominence in the classification program for nuclear C*-algebras of late, due primarily to the fact that Elliott's classification conjecture predicts that all simple, separable, and nuclear C*-algebras with unperforated K-theory will absorb Z tensorially (i.e., will be Z-stable). There exist counterexamples which suggest that the conjecture will only hold for simple, nuclear, separable and Z-stable C*-algebras. We prove that virtually all classes of nuclear C*-algebras for which the Elliott conjecture has been confirmed so far, consist of Z-stable C*-algebras. This result follows in large part from the following theorem, also proved herein: separable and approximately divisible C*-algebras are Z-stable.
19 pages

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Operator Algebras, Functional Analysis, K-Theory and Homology, 46L85; 46L35

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http://salesiana.dossiersoluciones.com/handle/123456789/76019

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0508218
 http://arxiv.org/abs/math/0508218

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arXiv