Classification of simple commutative algebras in the Delannoy category
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916023241801728 |
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| author | Etingof, Pavel Snowden, Andrew |
| author_facet | Etingof, Pavel Snowden, Andrew |
| contents | The Delannoy category is an interesting pre-Tannakian category associated to the oligomorphic group $\mathbb{G}$ of automorphisms of the totally ordered set $(\mathbf{R}, <)$. By construction, it admits some obvious simple commutative algebras, corresponding to certain transitive $\mathbb{G}$-sets. We show that these account for all of the simple commutative algebras in the Delannoy category. Previous results of this kind have been limited to interpolation categories; since the Delannoy category cannot be obtained by interpolation, new methods are required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of simple commutative algebras in the Delannoy category Etingof, Pavel Snowden, Andrew Representation Theory The Delannoy category is an interesting pre-Tannakian category associated to the oligomorphic group $\mathbb{G}$ of automorphisms of the totally ordered set $(\mathbf{R}, <)$. By construction, it admits some obvious simple commutative algebras, corresponding to certain transitive $\mathbb{G}$-sets. We show that these account for all of the simple commutative algebras in the Delannoy category. Previous results of this kind have been limited to interpolation categories; since the Delannoy category cannot be obtained by interpolation, new methods are required. |
| title | Classification of simple commutative algebras in the Delannoy category |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2511.18218 |