Abstract :
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.
