The path space of a directed graph
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- by Samuel B. G. Webster
- Proc. Amer. Math. Soc. 142 (2014), 213-225
- DOI: https://doi.org/10.1090/S0002-9939-2013-11755-7
- Published electronically: September 24, 2013
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Abstract:
We construct a locally compact Hausdorff topology on the path space of a directed graph $E$ and identify its boundary-path space $\partial E$ as the spectrum of a commutative $C^*$-subalgebra $D_E$ of $C^*(E)$. We then show that $\partial E$ is homeomorphic to a subset of the infinite-path space of any desingularisation $F$ of $E$. Drinen and Tomforde showed that we can realise $C^*(E)$ as a full corner of $C^*(F)$, and we deduce that $D_E$ is isomorphic to a corner of $D_F$. Lastly, we show that this isomorphism implements the homeomorphism between the boundary-path spaces.References
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Bibliographic Information
- Samuel B. G. Webster
- Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
- Email: sbgwebster@gmail.com
- Received by editor(s): February 6, 2011
- Received by editor(s) in revised form: March 1, 2012
- Published electronically: September 24, 2013
- Additional Notes: This research was supported by the ARC Discovery Project DP0984360.
- Communicated by: Marius Junge
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 213-225
- MSC (2010): Primary 46L05, 05C20
- DOI: https://doi.org/10.1090/S0002-9939-2013-11755-7
- MathSciNet review: 3119197