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Stability of $\boldsymbol{C^*}$-algebras associated to graphs

Author: Mark Tomforde
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1787-1795
MSC (2000): Primary 46L55
Published electronically: January 30, 2004
MathSciNet review: 2051143
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Abstract: We characterize stability of graph $C^*$-algebras by giving five conditions equivalent to their stability. We also show that if $G$ is a graph with no sources, then $C^*(G)$ is stable if and only if each vertex in $G$ can be reached by an infinite number of vertices. We use this characterization to realize the stabilization of a graph $C^*$-algebra. Specifically, if $G$ is a graph and $\tilde{G}$ is the graph formed by adding a head to each vertex of $G$, then $C^*(\tilde{G})$ is the stabilization of $C^*(G)$; that is, $C^*(\tilde{G}) \cong C^*(G) \otimes \mathcal{K}$.

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Additional Information

Mark Tomforde
Affiliation: Department of Mathematics, Dartmouth College, Hanover, New Hampshire 03755-3551
Address at time of publication: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242

Received by editor(s): June 14, 2002
Received by editor(s) in revised form: March 1, 2003
Published electronically: January 30, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society

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