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Journal of Operator Theory

Volume 76, Issue 1, Summer 2016  pp. 175-204.

Classification of tight $C^{*}$-algebras over the one-point compactification of $\mathbb{N}$

Authors:  James Gabe (1) and Efren Ruiz (2)
Author institution: (1) Department of Mathematics and Computer Science, The University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
(2) Department of Mathematics, University of Hawaii, Hilo, 200 W. Kawili St., Hilo, Hawaii, 96720-4091 U.S.A.

Summary:  We prove a strong classification result for a certain class of $C^{*}$-algebras with primitive ideal space $\widetilde{\mathbb{N}}$, where $\widetilde{\mathbb{N}}$ is the one-point compactification of $\mathbb{N}$. This class contains the class of graph $C^{*}$-algebras with primitive ideal space $\widetilde{\mathbb{N}}$. Along the way, we prove a universal coefficient theorem with ideal-related $K$-theory for $C^{*}$-algebras over $\widetilde{\mathbb{N}}$ whose $\infty$ fiber has torsion-free $K$-theory.

Keywords:  classification, continuous fields of $C^{*}$-algebras, $C^{*}$-algebras over $X$, graph $C^{*}$-algebras

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