# 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