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

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

   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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2. 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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3. Extensions of C *-Algebras by a Small Ideal

   https://doi.org/10.1093/imrn/rnac115  

   Lin, Huaxin; Ng, PingWong (May 2022, International Mathematics Research Notices)

   Abstract We classify all essential extensions of the form $$ \begin{align*} &0 \rightarrow {\mathcal{W}} \rightarrow {D} \rightarrow A \rightarrow 0,\end{align*}$$where $${\mathcal {W}}$$ is the unique separable simple C*-algebra with a unique tracial state, which is $KK$-contractible and has finite nuclear dimension, and $$A$$ is a separable amenable $${\mathcal {W}}$$-embeddable C*-algebra, which satisfies the Universal Coefficient Theorem (UCT). We actually prove more general results. We also classify a class of amenable $C^*$-algebras, which have only one proper closed ideal $${\mathcal {W}}.$$ 

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4. The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension

   https://doi.org/10.1016/j.geomphys.2020.103861  

   Elliott, G.A; Gong, G.; Lin, Huaxin; Niu, Z. (December 2020, Journal of geometry and physics)

   null (Ed.)

   The class of simple separable KK-contractible (KK-equivalent to \{0\} ) C*-algebra s which have finite nuclear dimension is shown to be classified by the Elliott invariant. In particular, the class of C*-algebras A\otimes K is classifiable, where A is a simple separable C*-algebra with finite nuclear dimension and is the simple inductive limit of Razak algebras with unique trace, which is bounded 

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5. Tracial approximation in simple $C*$-algebras

   https://doi.org/10.4153/S0008414X21000158  

   Fu, X.; Lin, H. (February 2021, Canadian journal of mathematics)

   We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable in nite dimensional C*-algebra A is asymptotically tracially in the class of C-algebras with nite nuclear dimension if and only if A is asymptotically tracially in the class of nuclear Z-stable C-algebras. 1 

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