The cycline subalgebra of a Kumjian-Pask algebra

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 ${\mathrm{KP}}_R(\Lambda )$. We also prove a generalized Cuntz-Krieger uniqueness theorem for Kumjian-Pask algebras which says that a representation of ${\mathrm{KP}}_R(\Lambda )$ is injective if and only if it is injective on $\mathcal{M}$.