$C^{\ast }$-exponential rank of unital simple classifiable $C^{\ast }$-algebras

Abstract

Let $\mathfrak{A}$ be the class of all unital simple separable amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras satisfying UCT, which are classified by Elliott invariant. In this paper, we proved that any $C^{\ast }$-algebra in $\mathfrak{A}$ has $C^{\ast }$-exponential rank at most $1+\epsilon$.