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

Takeshi Katsura, Aidan Sims, Mark Tomforde

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1589-1620
Number of pages32
JournalJournal of Functional Analysis
Volume257
Issue number5
DOIs
Publication statusPublished - 2009 Sep 1

Keywords

  • AF-algebras
  • Bratteli diagrams
  • Exel-Laca algebras
  • Graph C-algebras
  • Ultragraph C-algebras

ASJC Scopus subject areas

  • Analysis

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