Ordinal graphs and their $\mathrm{C}^{*}$-algebras
DOI:
https://doi.org/10.2140/mscand.2026.132.191Keywords:
ordinal, graph, Cuntz–Pimsner algebra, C*-correspondenceAbstract
We introduce a class of left cancellative categories we call ordinal graphs for which there is a functor $d:\Lambda\rightarrow\mathrm{Ord}$ by which morphisms of $\Lambda$ factor. We use generators and relations to study the Cuntz–Krieger algebra $\mathcal{O}(\Lambda)$ defined by Spielberg. In particular, we construct a $\mathrm{C}^{*}$-correspondence $X_{\alpha}$ for each $\alpha\in\mathrm{Ord}$ in order to apply Paulovicks and Tomforde's condition (S) and prove a Cuntz–Krieger uniqueness theorem for ordinal graphs.
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