2008/10/22 by Takeshi Katsura, Katsura, Takeshi, Aidan Sims +3
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.0810.4091
34 pages, Version 2 comments: Some minor typos corrected; Version 3 comments: Some typos corrected. This is the version to appear
arxiv created 2009/05/24 · arxiv updated 2009/12/01
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.