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Z-stable ASH algebras | | Andrew S. Toms
; Wilhelm Winter
; | | Date: |
12 Aug 2005 | | Subject: | Operator Algebras; Functional Analysis; K-Theory and Homology MSC-class: 46L85; 46L35 | math.OA math.FA math.KT | | 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. | | Source: | arXiv, math.OA/0508218 | | Services: | Forum | Review | PDF | Favorites | |
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