A classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras, I: $C^{\ast }$-algebras with generalized tracial rank one

Guihua Gong, Huaxin Lin, Zhuang Niu

A class of $C^{\ast }$-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 ame…