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