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arXiv · 1603.00508

The cycline subalgebra of a Kumjian-Pask algebra

Lisa Orloff Clark·Cristóbal Gil Canto·Alireza Nasr-Isfahani
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Abstract

Let $\Lambda$ be a row-finite higher-rank graph with no sources. We identify a maximal commutative subalgebra $\mathcal{M}$ inside the Kumjian-Pask algebra ${\rm KP}_R(\Lambda)$. We also prove a generalized Cuntz-Krieger uniqueness theorem for Kumjian-Pask algebras which says that a representation of ${\rm KP}_R(\Lambda)$ is injective if and only if it is injective on $\mathcal{M}$.

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Lisa Orloff Clark, Cristóbal Gil Canto, Alireza Nasr-Isfahani. 2016-03-01. The cycline subalgebra of a Kumjian-Pask algebra. https://arxiv.org/abs/1603.00508

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