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
Contents
Full-Text PDF