AF-embeddability of $2$-graph algebras and quasidiagonality of $k$-graph algebras

Abstract

We characterise quasidiagonality of the $C^{\ast }$-algebra of a cofinal $k$-graph in terms of an algebraic condition involving the coordinate matrices of the graph. This result covers all simple $k$-graph $C^{\ast }$-algebras. In the special case of cofinal $2$-graphs we further prove that AF-embeddability, quasidiagonality and stable finiteness of the $2$-graph algebra are all equivalent.

This is the version that is to appear in the Journal of Functional Analysis. The title has changed

References in corpus (4)

• Simplicity of C*-algebras associated to higher-rank graphs
• The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources
• Purely infinite $C^{\ast }$-algebras associated to étale groupoids
• AF-Embeddings of Graph Algebras