 

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. 


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.


Acknowledgements
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/

