A classification of finite simple amenable Z-stable C^*-algebras, I: C^*-algebras with generalized tracial rank one · arXivDesk
1812.11590Dec 30, 2018This is a part I of a revision of the original arXiv:1501.00135. This paper has been accepted and will appear in C. R. Math. Acad. Sci. Soc. R. Canada
A classification of finite simple amenable Z-stable C∗-algebras, I: C∗-algebras with generalized tracial rank one
A class of C∗-algebras, to be called those of generalized tracial rank one, is introduced, and classified by the Elliott invariant. A second class of unital simple separable amenable C∗-algebras, those whose tensor products with UHF-algebras of infinite type are in the first class, to be referred to as those of rational generalized tracial rank one, is proved to exhaust all possible values of the Elliott invariant for unital finite simple separable amenable Z-stable C∗
Nearby in the stack
-algebras. An isomorphism theorem for a special sub-class of those
C∗
-algebras are presented. This provides the basis for the classification of
C∗
-algebras with rational generalized tracial rank one in Part II.
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