Z-stable ASH algebras

Details Z-stable ASH algebras Z-stable ASH algebras

2005-08-12

arxiv.org/abs/math/0508218v1

Mathematics

Operator Algebras

19 pages

Scientific paper

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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