Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The path space of a directed graph


Author: Samuel B. G. Webster
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
Published electronically: September 24, 2013
MathSciNet review: 3119197
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46L05, 05C20

Retrieve articles in all journals with MSC (2010): 46L05, 05C20


Additional Information

Samuel B. G. Webster
Affiliation: School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
Email: sbgwebster@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11755-7
Keywords: Graph algebra, directed graph, path space, boundary paths
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.