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Inductive limits of subhomogeneous C ∗ -algebras with Hausdorff spectrum

2009; Elsevier BV; Volume: 258; Issue: 6 Linguagem: Inglês

10.1016/j.jfa.2009.06.036

1096-0783

Huaxin Lin,

Advanced Banach Space Theory

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 ⊗ 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 ≅ B if and only if they have the same Elliott invariant.