On the classification of simple amenable C*-algebras with finite decomposition rank

Abstract

Let $A$ be a unital simple separable C*-algebra satisfying the UCT. Assume that $\mathrm{dr}(A)<+\infty$, $A$ is Jiang-Su stable, and ${\mathrm{K}}_0(A)\otimes \mathbb{Q}\cong \mathbb{Q}$. Then $A$ is an ASH algebra (indeed, $A$ is a rationally AH algebra).

10 pages; Part I of arXiv:1507.03437; To appear in "Operator Algebras and their Applications: A Tribute to Richard V. Kadison", Contemporary Mathematics, Amer. Math. Soc., Providence, R. I., 2016