Viewing AF-algebras as graph algebras
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- by D. Drinen PDF
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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 Strǎtilǎ 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 $A$.References
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Additional Information
- D. Drinen
- Affiliation: Department of Mathematics, Arizona State University, Tempe, Arizona 85287
- Email: Drinen@asu.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1991-2000
- MSC (1991): Primary 46L05; Secondary 22A22
- DOI: https://doi.org/10.1090/S0002-9939-99-05286-7
- MathSciNet review: 1657723