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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.11431 |
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| _version_ | 1866908770985050112 |
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| author | Edie-Michell, Cain Katumba, Jacques |
| author_facet | Edie-Michell, Cain Katumba, Jacques |
| contents | We define a notion of super-transitivity for ètale algebra objects $A \in \mathcal{C}(\mathfrak{sl}_N, k)$. This definition is a direct analogue of the notion of super-transitivity for subfactors, and measures at what depth the first ``new stuff'' appears in the category of $A$-modules internal to $\mathcal{C}(\mathfrak{sl}_N, k)$. Our main theorem gives a classification of all 1-super-transitive ètale algebra objects in $\mathcal{C}(\mathfrak{sl}_N, k)$ running over all $N,k \in \mathbb{N}$. Our classification captures all known infinite families of non-pointed ètale algebras in $\mathcal{C}(\mathfrak{sl}_N, k)$, and includes all but 16 of the known non-pointed ètale algebra objects in these categories. These remaining 16 known examples have super-transitivities between 2 and 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of 1-super-transitive quantum subgroups in type A Edie-Michell, Cain Katumba, Jacques Quantum Algebra We define a notion of super-transitivity for ètale algebra objects $A \in \mathcal{C}(\mathfrak{sl}_N, k)$. This definition is a direct analogue of the notion of super-transitivity for subfactors, and measures at what depth the first ``new stuff'' appears in the category of $A$-modules internal to $\mathcal{C}(\mathfrak{sl}_N, k)$. Our main theorem gives a classification of all 1-super-transitive ètale algebra objects in $\mathcal{C}(\mathfrak{sl}_N, k)$ running over all $N,k \in \mathbb{N}$. Our classification captures all known infinite families of non-pointed ètale algebras in $\mathcal{C}(\mathfrak{sl}_N, k)$, and includes all but 16 of the known non-pointed ètale algebra objects in these categories. These remaining 16 known examples have super-transitivities between 2 and 4. |
| title | Classification of 1-super-transitive quantum subgroups in type A |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2601.11431 |