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arXiv · 1203.2815

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

Pere Ara
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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 $C^*_{\text{red}} (E,C)$. 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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Pere Ara. 2012-03-13. Purely infinite simple reduced C*-algebras of one-relator separated graphs. https://arxiv.org/abs/1203.2815

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