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Published: 
February 1, 2000

Keywords: 
Graphs as categories, Graph algebra, Path groupoid, C*algebra

Subject: 
Primary 46L05; Secondary 46L55.

Abstract:

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.

Acknowledgments:
Research of the first author partially supported by NSF grant DMS9706982
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 895570045, USA.
alex@unr.edu
http://equinox.comnet.unr.edu/homepage/alex/
David Pask:
Department of Mathematics, University of Newcastle, NSW 2308, Australia
davidp@maths.newcastle.edu.au
http://maths.newcastle.edu.au/~davidp/
 