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 arises as the -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 coincides with Kumjian's twist groupoid constructed from a diagonal of .

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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

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