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

Pere Ara

doi:10.1016/j.jmaa.2012.04.014

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

Pere Ara

Research output: Contribution to journal › Article › Research › peer-review

6 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 language	English
Pages (from-to)	493-508
Journal	Journal of Mathematical Analysis and Applications
Volume	393
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.04.014
Publication status	Published - 15 Sept 2012

Keywords

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

Access to Document

10.1016/j.jmaa.2012.04.014

Cite this

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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 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. {\textcopyright} 2012 Elsevier Ltd.",

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AB - 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.

KW - Amalgamated free product

KW - Conditional expectation

KW - Graph c -algebra

KW - Purely infinite

KW - Separated graph

KW - Simple

U2 - 10.1016/j.jmaa.2012.04.014

DO - 10.1016/j.jmaa.2012.04.014

M3 - Article

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EP - 508

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2