 

Hui Li, David Pask, and Aidan Sims
An elementary approach to C*algebras associated to topological graphs view print


Published: 
May 17, 2014

Keywords: 
C*algebra; graph algebra; C*correspondence; topological graph; CuntzPimsner algebra 
Subject: 
46L05 


Abstract
We develop notions of a representation of a topological graph E and of a covariant
representation of a topological graph E which do not require the machinery of
C*correspondences and CuntzPimsner algebras. We show that the C*algebra
generated by a universal representation of E is isomorphic to the Toeplitz algebra of
Katsura's topologicalgraph bimodule, and that the C*algebra generated by a universal
covariant representation of E is isomorphic to Katsura's topological graph
C*algebra. We exhibit our results by constructing the isomorphism between the
C*algebra of a rowfinite directed graph E with no sources and the C*algebra of
the topological graph arising from the shift map acting on the infinitepath space
E^{∞}.


Acknowledgements
This research was supported by the Australian Research Council.


Author information
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong NSW 2522, AUSTRALIA
hl338@uowmail.edu.au
dpask@uow.edu.au
asims@uow.edu.au

