arXiv 0810.40912008-10math.OA

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

Takeshi Katsura, Aidan Sims, Mark Tomforde

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

英文摘要：

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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