Classification of finite simple amenable $\mathcal{Z}$-stable $C^*$-algebras

Huaxin Lin

10:50 am to 11:40 am, June 2nd, 2015   Science Building A510

Abstract:

We present a classification theorem for a class of unital simple separable amenable $\mathcal{Z}$-stable $C^*$-algebras by the Elliott invariant. This class of simple $C^*$-algebras exhausts all possible values of Elliott invariant for unital stably finite simple separable amenable $\mathcal{Z}$-stable $C^*$-algebras. Moreover, it contains all unital simple separable amenable $C^*$-algebras which satisfy the UCT and have finite rational tracial rank.