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

2015/08/11 by Lisa Orloff Clark, Clark, Lisa Orloff, Astrid an Huef +3 · 1 citation
Mathematics · #46L05 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.1508.02746

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

arxiv created 2016/05/08 · arxiv updated 2016/05/10

Abstract

We characterise quasidiagonality of the C^*-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^*-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.

Cited by

• Nuclear dimension, pure infiniteness and real rank for higher rank graph C^*-algebras

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