The range of a class of classifiable separable simple amenable C ∗-algebras

We study the range of a classifiable class A of unital separable simple amenable C ∗-algebras which satisfy the Universal Coefficient Theorem. The class A contains all unital simple AH-algebras. We show that all unital simple inductive limits of dimension drop circle C ∗-algebras are also in the class. This unifies some of the previous known classification results for unital simple amenable C ∗-algebras. We also show that there are many other C ∗-algebras in the class. We prove that, for any partially ordered simple weakly unperforated rationally Riesz group G0 with order unit u, any countable abelian group G1, any metrizable Choquet simplex S, and any surjective affine continuous map r : S →Su(G0) (where Su(G0) is the state space of G0) which preserves extremal points, there exists one and only one (up to isomorphism) unital separable simple amenable C ∗-algebra A in the classifiable class A such that K0(A),K0(A)+, [1A ] ,K1(A), T (A), λA = G0, (G0)+,u ,G1,S, r . © 2010 Elsevier Inc. All rights reserved.