Z-stable ASH algebras

Andrew S. Toms; Wilhelm Winter

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arXiv · math/0508218

Z-stable ASH algebras

Andrew S. Toms·Wilhelm Winter

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Abstract

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.

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BibTeX RIS

Andrew S. Toms, Wilhelm Winter. 2005-08-12. Z-stable ASH algebras. https://arxiv.org/abs/math/0508218

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