Classification of Simple Tracially AF C *-Algebras

By Huaxin Lin. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2001

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Classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras (2014, background): “There is also the classification of unital simple amenable C*-algebras in the UCT class which have finite tracial rank ([47], [53] , [57] and [67]).”
On tracial approximation (2008, background): “Instead of assuming inductive limit structure, he started with a certain abstract approximation property, and showed that C*-algebras with this abstract approximation property and certain additional properties are AH-algebras without dimension growth [18, 20,21,23].”
A classification of finite simple amenable ${\cal Z}$-stable $C^*$-algebras, I: $C^*$-algebras with generalized tracial rank one. (2018, background): “These efforts became the engine for these rapid developments ([55], [51], [60] and [16] for example).”
Recasting the Elliott conjecture (2006, background): “An exhaustive list of these results would be impossibly long, but some of the most important include [8], [10], [11], [12], and [22].”