New York Journal of Mathematics
Volume 6 (2000) 1-20


Alex Kumjian and David Pask

Higher Rank Graph C*-Algebras

Published: February 1, 2000
Keywords: Graphs as categories, Graph algebra, Path groupoid, C*-algebra
Subject: Primary 46L05; Secondary 46L55.

Building on recent work of Robertson and Steger, we associate a C*-algebra to a combinatorial object which may be thought of as a higher rank graph. This C*-algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C*-algebra to be: simple, purely infinite and AF. Results concerning the structure of crossed products by certain natural actions of discrete groups are obtained; a technique for constructing rank 2 graphs from "commuting'' rank 1 graphs is given.


Research of the first author partially supported by NSF grant DMS-9706982
Research of the second author supported by University of Newcastle RMC project grant

Author information

Alex Kumjian:
Department of Mathematics (084), University of Nevada, Reno NV 89557-0045, USA.

David Pask:
Department of Mathematics, University of Newcastle, NSW 2308, Australia