Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras

Details Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras Realizations of AF-algebras as graph algebras, Exel-Laca algebras, and ultragraph algebras

2008-10-22

arxiv.org/abs/0810.4091v3

Mathematics

Operator Algebras

34 pages, Version 2 comments: Some minor typos corrected; Version 3 comments: Some typos corrected. This is the version to app

Scientific paper

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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