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arXiv · 2111.15165

Stably finite extensions of rank-two graph C*-algebras

Astrid an Huef·Abraham C. S. Ng·Aidan Sims
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Abstract

We study stable finiteness of extensions of 2-graph C*-algebras determined by saturated hereditary sets of vertices. We use two iterations of the Pimsner-Voiculescu sequence to calculate the map in K-theory induced by the inclusion of a hereditary subgraph into the larger 2-graph it lives in. We then apply a theorem of Spielberg about stable finiteness of extensions to provide a sufficient condition for the C*-algebra of the larger 2-graph to be stably finite. We illustrate our results with examples.

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Astrid an Huef, Abraham C. S. Ng, Aidan Sims. 2021-11-30. Stably finite extensions of rank-two graph C*-algebras. https://arxiv.org/abs/2111.15165

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