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

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

2012-03-13

arxiv.org/abs/1203.2815v1

Mathematics

Operator Algebras

25 pages

Scientific paper

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 $C^*_{\text{red}} (E,C)$. For a large class of separated graphs $(E,C)$, we prove that $C^*_{\text{red}} (E,C)$ 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.

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