AF Embedding of Crossed Products of Certain Graph C^*-Algebras by Quasi-free Actions

2005/10/26 by Fang, Xiaochun
#19K33 #46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0510551

Abstract

We introduce the labelling map and the quasi-free action of a locally compact abelian group on a graph C^*-algebra of a row-finite directed graph. Some necessary conditions for embedding the crossed product to an AF algebra are discussed, and one sufficient condition is proved that if the row-finite directed graph is constructed by possibly attaching some 1-loops to a row-finite directed graph whose each weak connected component is a rooted (possibly infinite) directed tree, and the labelling map is almost proper, which is proved to be a reasonable generalization of the earlier case, then the crossed product can be embedded to an AF algebra.

Related

• C^*-algebras associated to directed graphs of groups, and models of Kirchberg algebras
• AF-embeddability of crossed products of Cuntz algebras
• Coverings of Directed Graphs and Crossed Products of C*-algebras by Coactions of Homogeneous Spaces
• Group Actions on Product Systems
• Simplicity of twisted C*-algebras of higher-rank graphs and crossed\n products by quasifree actions