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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Cuntz-Krieger algebras of infinite graphs and matrices
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by Iain Raeburn and Wojciech Szymański PDF
Trans. Amer. Math. Soc. 356 (2004), 39-59 Request permission

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 Szymański
  • Affiliation: Department of Mathematics, University of Newcastle, New South Wales 2308, Australia
  • Email: wojciech@frey.newcastle.edu.au
  • Received by editor(s): December 15, 1999
  • Published electronically: August 21, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 39-59
  • MSC (2000): Primary 46L05
  • DOI: https://doi.org/10.1090/S0002-9947-03-03341-5
  • MathSciNet review: 2020023