Abstract
We give various necessary and sufficient conditions for an AF-algebra to be isomorphic to a graph C ∗ -algebra, an Exel–Laca algebra, and an ultragraph C ∗ -algebra. We also explore consequences of these results. In particular, we show that all stable AF-algebras are both graph C ∗ -algebras and Exel–Laca algebras, and that all simple AF-algebras are either graph C ∗ -algebras or Exel–Laca algebras. In addition, we obtain a characterization of AF-algebras that are isomorphic to the C ∗ -algebra of a row-finite graph with no sinks.
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