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arXiv · 1508.02746

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

Lisa Orloff Clark·Astrid an Huef·Aidan Sims
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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.

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Lisa Orloff Clark, Astrid an Huef, Aidan Sims. 2015-08-11. AF-embeddability of $2$-graph algebras and quasidiagonality of $k$-graph algebras. https://arxiv.org/abs/1508.02746

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