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arXiv · 1512.06547

Kumjian-Pask algebras of finitely-aligned higher-rank graphs

Lisa Orloff Clark·Yosafat E. P. Pangalela
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Abstract

We extend the the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and have a graded uniqueness theorem. We also prove the Cuntz-Kreiger uniqueness theorem; to do this, we use a groupoid approach. As a consequence of the graded uniqueness theorem, we show that every Kumjian-Pask algebra is isomorphic to the Steinberg algebra associated to its boundary path groupoid. We then use Steinberg algebra results to prove the Cuntz-Kreiger uniqueness theorem and also to characterize simplicity and basic simplicity.

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Lisa Orloff Clark, Yosafat E. P. Pangalela. 2015-12-21. Kumjian-Pask algebras of finitely-aligned higher-rank graphs. https://arxiv.org/abs/1512.06547

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