$C^*$-correspondences for ordinal graphs
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866908837307482112 |
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| author | Jones, Benjamin |
| author_facet | Jones, Benjamin |
| contents | We introduce a family of $C^*$-correspondences $X_α$ naturally associated to every ordinal graph $Λ$. When $Λ$ is a directed graph, $X_0$ is isomorphic to the usual $C^*$-correspondence associated to a graph. We show that ordinal graphs satisfying a weak assumption have the property that the $C^*$-algebra of $Λ_{α+ 1}$ is isomorphic to the Cuntz-Pimsner algebra of $X_α$. As a consequence, the $C^*$-algebra of $Λ$ may be constructed starting from $c_0(Λ_0)$ by iteratively applying the Cuntz-Pimsner construction and inductive limits. We apply this result to strengthen the author's previous Cuntz-Krieger uniqueness theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15148 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $C^*$-correspondences for ordinal graphs Jones, Benjamin Operator Algebras 46L05 (Primary) 46L08 (Secondary) We introduce a family of $C^*$-correspondences $X_α$ naturally associated to every ordinal graph $Λ$. When $Λ$ is a directed graph, $X_0$ is isomorphic to the usual $C^*$-correspondence associated to a graph. We show that ordinal graphs satisfying a weak assumption have the property that the $C^*$-algebra of $Λ_{α+ 1}$ is isomorphic to the Cuntz-Pimsner algebra of $X_α$. As a consequence, the $C^*$-algebra of $Λ$ may be constructed starting from $c_0(Λ_0)$ by iteratively applying the Cuntz-Pimsner construction and inductive limits. We apply this result to strengthen the author's previous Cuntz-Krieger uniqueness theorem. |
| title | $C^*$-correspondences for ordinal graphs |
| topic | Operator Algebras 46L05 (Primary) 46L08 (Secondary) |
| url | https://arxiv.org/abs/2602.15148 |