# 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.

**DOI: **http://dx.doi.org/10.7900/jot.2015nov30.2086

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

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