A dichotomy for simple self-similar graph C^∗-algebras

2020/05/12 by Larki, Hossein
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2005.05543

Abstract

We investigate the pure infiniteness and stable finiteness of the Exel-Pardo C^*-algebras O_G,E for countable self-similar graphs (G,E,φ). In particular, we associate a specific ordinary graph \widetildeE to (G,E,φ) such that some properties such as simpleness, stable finiteness or pure infiniteness of the graph C^*-algebra C^*(\widetildeE) imply that of O_G,E. Among others, this follows a dichotomy for simple O_G,E: if (G,E,φ) contains no G-circuits, then O_G,E is stably finite; otherwise, O_G,E is purely infinite. Furthermore, Li and Yang recently introduced self-similar k-graph C^*-algebras O_G,Λ. We also show that when |Λ⁰|

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• Self-Similar k-Graph C*-Algebras
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