2015/04/14 by Jeong, Ja A, Kang, Eun Ji, Kim, Sun Ho +1
#37A55 #46L05 #46L55 #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1504.03455
It is now well known that a simple graph C^*-algebra C^*(E) of a directed graph E is either AF or purely infinite. In this paper, we address the question of whether this is the case for labeled graph C^*-algebras recently introduced by Bates and Pask as one of the generalizations of graph C^*-algebras, and show that there exists a family of simple unital labeled graph C^*-algebras which are neither AF nor purely infinite. Actually these algebras are shown to be isomorphic to crossed products C(X)×T \mathbb Z where the dynamical systems (X,T) are Cantor minimal subshifts. Then it is an immediate consequence of well known results about this type of crossed products that each labeled graph C^*-algebra in the family obtained here is an A\mathbb T algebra with real rank zero and has \mathbb Z as its K1-group.