Stability of $\boldsymbol {C^*}$-algebras associated to graphs
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- by Mark Tomforde PDF
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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, $C^*(\tilde {G}) \cong C^*(G) \otimes \mathcal {K}$.References
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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
- MR Author ID: 687274
- Email: tomforde@math.uiowa.edu
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1787-1795
- MSC (2000): Primary 46L55
- DOI: https://doi.org/10.1090/S0002-9939-04-07411-8
- MathSciNet review: 2051143