Inductive Limits of Subhomogeneous $C^{\ast }$-algebras with Hausdorff Spectrum

Abstract

We consider unital simple inductive limits of generalized dimension drop C*-algebras They are so-called ASH-algebras and include all unital simple AH-algebras and all dimension drop $C^{\ast }$-algebras. Suppose that $A$ is one of these C*-algebras. We show that $A\otimes Q$ has tracial rank no more than one, where $Q$ is the rational UHF-algebra. As a consequence, we obtain the following classification result: Let $A$ and $B$ be two unital simple inductive limits of generalized dimension drop algebras with no dimension growth. Then $A\cong B$ if and only if they have the same Elliott invariant.

References in corpus (3)

• Localizing the Elliott conjecture at strongly self-absorbing C*-algebras
• On the classification problem for nuclear C*-algebras
• The Range of a Class of Classifiable Separable Simple Amenable C*-Algebras

Cited by in corpus (1)

• A generalization of the Jiang-Su construction