TY - JOUR
T1 - Purely infinite simple reduced C *-algebras of one-relator separated graphs
AU - Ara, Pere
PY - 2012/9/15
Y1 - 2012/9/15
N2 - 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.
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
UR - https://www.scopus.com/pages/publications/84860915536
U2 - 10.1016/j.jmaa.2012.04.014
DO - 10.1016/j.jmaa.2012.04.014
M3 - Article
SN - 0022-247X
VL - 393
SP - 493
EP - 508
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -