Ordinal graphs and their $\mathrm{C}^*$-algebras

Benjamin Jones

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arXiv · 2411.00206

Ordinal graphs and their $\mathrm{C}^*$-algebras

Benjamin Jones

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Abstract

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 $\mathcal{O}\left(\Lambda\right)$ defined by Spielberg. In particular, we construct a $\mathrm{C}^{*}$-correspondence $X_{\alpha}$ for each $\alpha\in\mathrm{Ord}$ in order to apply Ery\"uzl\"u and Tomforde's condition (S) and prove a Cuntz-Krieger uniqueness theorem for ordinal graphs.

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Benjamin Jones. 2024-10-31. Ordinal graphs and their $\mathrm{C}^*$-algebras. https://arxiv.org/abs/2411.00206

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