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2. A classification of finite simple amenable Z-stable C*-algebras, II: C*-algebras with rational generalized tracial rank one

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   Elliott, G.A. (Ed.)

   A classification theorem is obtained for a class of unital simple separable amenable Z-stable C*-algebras which exhausts all possi- ble values of the Elliott invariant for unital stably finite simple separable amenable Z-stable C*-algebras. Moreover, it contains all unital simple separable amenable C∗-algebras which satisfy the UCT and have finite rational tracial rank. 

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3. A classification of finite simple amenable Z-stable C*-algebras, II: C*-algebras with rational generalized tracial rank one

   Gong, Guihua ; Lin, Huaxin ; Niu, Zhuang ( October 2020 , Comptes Rendus MathéMatiques de LacadéMie des Sciences)

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4. A classification of finite simple amenable Z-stable C∗-algebras, I: C*-algebras with generalized tracial rank one

   Gong, G. ; Lin, Huaxin ; Niu, Z. ( December 2020 , C. R. Math. Rep. Acad. Sci. Canada)

   Elliott, G.A. (Ed.)

   A class of C*-algebras, to be called those of generalized tracial rank one, is introduced. 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*- algebras. A number of results toward the classification of the second class are presented including an isomorphism theorem for a special sub-class of the first class, leading to the general classification of all unital simple C*- algebras with rational generalized tracial rank one in Part II. 

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