Classification of simple commutative algebras in the Delannoy category

2025/11/22 by Etingof, Pavel, Snowden, Andrew
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.18218

openalex publication_date 2025/11/22 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

The Delannoy category is an interesting pre-Tannakian category associated to the oligomorphic group \mathbbG of automorphisms of the totally ordered set (R, <). By construction, it admits some obvious simple commutative algebras, corresponding to certain transitive \mathbbG-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.

Citations

• A characterization of the Delannoy category by Adams operations
• Classical interpolation categories
• Discrete pre-Tannakian categories
• Pre-Galois categories and Fraïssé's theorem
• Oligomorphic groups and tensor categories
• Classification of simple algebras in Deligne category Rep(S_t)
• Deligne categories as limits in rank and characteristic
• Simple commutative algebras in Deligne's categories Rep(S_t)

Cited by

• Universal properties of Delannoy categories

Related

• The Delannoy category
• A characterization of the Delannoy category by Adams operations
• Universal properties of Delannoy categories
• The circular Delannoy category
• Simple commutative algebras in Deligne's categories Rep(S_t)