Journal of Operator Theory
Volume 74, Issue 1, Summer 2015 pp. 177-182.
AF-embeddings of graph $C^*$-algebras
Authors:
Christopher P. Schafhauser
Author institution:Department of Mathematics, University of Nebraska -
Lincoln, Lincoln, NE 68508, U.S.A.
Summary: Let $E$ be a countable directed graph. We show that
for the algebra $C^*(E)$ the properties of being AF-embeddable,
quasidiagonal, stably finite, and finite are equivalent and that these
properties hold if and only if no cycle in $E$ has an entrance. In this
case, we present a construction, in the spirit of the Drinen--Tomforde
desingularization, that allows one to embed $C^*(E)$ into a AF graph
algebra.
DOI: http://dx.doi.org/10.7900/jot.2014may23.2017
Keywords: graph algebras, AF-embeddability, quasidiagonality
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