Ordinal graphs and their $\mathrm{C}^*$-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910788890918912 |
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| author | Jones, Benjamin |
| author_facet | Jones, Benjamin |
| contents | We introduce a class of left cancellative categories we call ordinal graphs for which there is a functor $d:Λ\rightarrow\mathrm{Ord}$ by which morphisms of $Λ$ factor. We use generators and relations to study the Cuntz-Krieger algebra $\mathcal{O}\left(Λ\right)$ defined by Spielberg. In particular, we construct a $\mathrm{C}^{*}$-correspondence $X_α$ for each $α\in\mathrm{Ord}$ in order to apply Eryüzlü and Tomforde's condition (S) and prove a Cuntz-Krieger uniqueness theorem for ordinal graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ordinal graphs and their $\mathrm{C}^*$-algebras Jones, Benjamin Operator Algebras 46L05 We introduce a class of left cancellative categories we call ordinal graphs for which there is a functor $d:Λ\rightarrow\mathrm{Ord}$ by which morphisms of $Λ$ factor. We use generators and relations to study the Cuntz-Krieger algebra $\mathcal{O}\left(Λ\right)$ defined by Spielberg. In particular, we construct a $\mathrm{C}^{*}$-correspondence $X_α$ for each $α\in\mathrm{Ord}$ in order to apply Eryüzlü and Tomforde's condition (S) and prove a Cuntz-Krieger uniqueness theorem for ordinal graphs. |
| title | Ordinal graphs and their $\mathrm{C}^*$-algebras |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/2411.00206 |