Inductive Limits of Subhomogeneous $C^*$-algebras with Hausdorff Spectrum

Details Inductive Limits of Subhomogeneous $C^*$-algebras with Hausdorff Spectrum Inductive Limits of Subhomogeneous $C^*$-algebras with Hausdorff Spectrum

2008-09-30

arxiv.org/abs/0809.5273v2

Mathematics

Operator Algebras

Scientific paper

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 $C^*$-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.

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