 

Aidan Sims
The couniversal C*algebra of a rowfinite graph view print


Published: 
November 22, 2010 
Keywords: 
Graph algebra, CuntzKrieger algebra 
Subject: 
Primary 46L05 


Abstract
Let E be a rowfinite directed graph. We prove that there
exists a C*algebra C*_{min}(E) with the following couniversal
property: given any C*algebra B generated by a
ToeplitzCuntzKrieger Efamily in which all the vertex
projections are nonzero, there is a canonical homomorphism from
B onto C*_{min}(E). We also identify when a homomorphism from
B to C*_{min}(E) obtained from the couniversal property is
injective. When every loop in E has an entrance, C*_{min}(E)
coincides with the graph C*algebra C*(E), but in
general, C*_{min}(E) is a quotient of C*(E). We investigate the
properties of C*_{min}(E) with emphasis on the utility of
couniversality as the defining property of the algebra.


Acknowledgements
This research was supported by the Australian Research Council.


Author information
School of Mathematics and Applied Statistics, Austin Keane Building (15), University of Wollongong, NSW 2522, AUSTRALIA
asims@uow.edu.au

