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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cuntz-Krieger algebras of infinite graphs and matrices


Authors: Iain Raeburn and Wojciech Szymanski
Journal: Trans. Amer. Math. Soc. 356 (2004), 39-59
MSC (2000): Primary 46L05
Published electronically: August 21, 2003
MathSciNet review: 2020023
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Abstract: We show that the Cuntz-Krieger algebras of infinite graphs and infinite $\{0,1\}$-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness theorems for Cuntz-Krieger algebras and to compute their $K$-theory. Since the finite approximating graphs have sinks, we have to calculate the $K$-theory of Cuntz-Krieger algebras of graphs with sinks, and the direct methods we use to do this should be of independent interest.


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Additional Information

Iain Raeburn
Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
Email: iain@frey.newcastle.edu.au

Wojciech Szymanski
Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
Email: wojciech@frey.newcastle.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03341-5
PII: S 0002-9947(03)03341-5
Received by editor(s): December 15, 1999
Published electronically: August 21, 2003
Article copyright: © Copyright 2003 American Mathematical Society