New York Journal of Mathematics
Volume 16 (2010) 507-524


Aidan Sims

The co-universal C*-algebra of a row-finite graph

view    print

Published: November 22, 2010
Keywords: Graph algebra, Cuntz-Krieger algebra
Subject: Primary 46L05

Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*min(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family 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 co-universal 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 co-universality as the defining property of the algebra.


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