Purely infinite simple reduced C *-algebras of one-relator separated graphs

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5 Citations (Scopus)

Abstract

Given a separated graph (E, C), there are two different C *-algebras associated to it: the full graph C *-algebra C *(E, C) and the reduced one Cred*(E,C). For a large class of separated graphs (E, C), we prove that Cred*(E,C) either is purely infinite simple or admits a faithful tracial state. The main tool we use to show pure infiniteness of reduced graph C *-algebras is a generalization to the amalgamated case of a result on purely infinite simple free products due to Dykema. © 2012 Elsevier Ltd.
Original languageEnglish
Pages (from-to)493-508
JournalJournal of Mathematical Analysis and Applications
Volume393
Issue number2
DOIs
Publication statusPublished - 15 Sep 2012

Keywords

  • Amalgamated free product
  • Conditional expectation
  • Graph c -algebra *
  • Purely infinite
  • Separated graph
  • Simple

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