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C*-Algebras of Infinite Graphs and Cuntz-Krieger Algebras

Published online by Cambridge University Press:  20 November 2018

Berndt Brenken
Berndt Brenken*
Affiliation:
Department of Mathematics & Statistics University of Calgary Calgary, Alberta T2N 1N4
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Abstract

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The Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ is defined for an arbitrary, possibly infinite and infinite valued, matrix $B$. A graph ${{C}^{*}}$-algebra ${{G}^{*}}\left( E \right)$ is introduced for an arbitrary directed graph $E$, and is shown to coincide with a previously defined graph algebra ${{C}^{*}}\left( E \right)$ if each source of $E$ emits only finitely many edges. Each graph algebra ${{G}^{*}}\left( E \right)$ is isomorphic to the Cuntz-Krieger algebra ${{\mathcal{O}}_{B}}$ where $B$ is the vertex matrix of $E$.

Keywords

46LXX05C50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 3 , 01 September 2002 , pp. 321 - 336
Copyright
Copyright © Canadian Mathematical Society 2002

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