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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Viewing AF-algebras as graph algebras


Author: D. Drinen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1991-2000
MSC (1991): Primary 46L05; Secondary 22A22
Published electronically: November 1, 1999
MathSciNet review: 1657723
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Abstract: Every AF-algebra $A$ arises as the $C^*$-algebra of a locally finite pointed directed graph in the sense of Kumjian, Pask, Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by Stratila and Voiculescu is consistent with Kumjian's notion of diagonal, and the groupoid arising from a well-chosen Bratteli diagram for $A$ coincides with Kumjian's twist groupoid constructed from a diagonal of $A$.


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Additional Information

D. Drinen
Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287
Email: Drinen@asu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05286-7
PII: S 0002-9939(99)05286-7
Received by editor(s): March 23, 1998
Received by editor(s) in revised form: August 18, 1998
Published electronically: November 1, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society