The Range of a Class of Classifiable Separable Simple Amenable C*-Algebras

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dc.creatorLin, Huaxin
dc.creatorNiu, Zhuang
dc.date2008-08-26
dc.date.accessioned2026-07-07T09:58:25Z
dc.date.available2026-07-07T09:58:25Z
dc.descriptionWe study the range of a classifiable class ${\cal A}$ of unital separable simple amenable $C^*$-algebras which satisfy the Universal Coefficient Theorem. The class ${\cal A}$ 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 $G_0$ with order unit $u,$ any countable abelian group $G_1,$ any metrizable Choquet simplex $S,$ and any surjective affine continuous map $r: S\to S_u(G_0)$ (where $S_u(G_0)$ is the state space of $G_0$) which preserves extremal points, there exists one and only one (up to isomorphism) unital separable simple amenable $C^*$-algebra $A$ in the classifiable class ${\cal A}$ such that $$ ((K_0(A), K_0(A)_+, [1_A]), K_1(A), T(A), λ_A)=((G_0, (G_0)_+, u), G_1,S, r).
dc.identifierhttps://arxiv.org/abs/0808.3424
dc.identifierhttp://arxiv.org/abs/0808.3424
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167712
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L05, 46L35, 46L80
dc.titleThe Range of a Class of Classifiable Separable Simple Amenable C*-Algebras
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