Vertex-transitive quantum graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917546929684480 |
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| author | Hayes, Mac Jess, Trevor Kornell, Andre Schmeis, Remi Salinas |
| author_facet | Hayes, Mac Jess, Trevor Kornell, Andre Schmeis, Remi Salinas |
| contents | We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vertex-transitive quantum graphs Hayes, Mac Jess, Trevor Kornell, Andre Schmeis, Remi Salinas Operator Algebras Combinatorics Quantum Algebra Quantum Physics 46L89, 47L05, 81P47, 05C75, 46L07 We define a quantum graph to be vertex-transitive if the join of its automorphism group is the maximum quantum relation on its quantum vertex set, in direct analogy with the classical case. All simple quantum graphs in $M_2(\mathbb C)$ are vertex-transitive, but many simple quantum graphs in $M_3(\mathbb C)$ are not vertex-transitive. We provide a complete classification of vertex-transitive quantum graphs in $M_3(\mathbb C)$ up to isomorphism. To do this, we introduce a polynomial invariant for quantum graphs in $M_n(\mathbb C)$, which we call the panoramic polynomial. |
| title | Vertex-transitive quantum graphs |
| topic | Operator Algebras Combinatorics Quantum Algebra Quantum Physics 46L89, 47L05, 81P47, 05C75, 46L07 |
| url | https://arxiv.org/abs/2605.30730 |