Matroids, Feynman categories, and Koszul duality

2022/11/22 by Basile Coron, Coron, Basile · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2211.12370

openalex publication_date 2022/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we introduce and study in detail. In addition, we establish a Koszul-type duality between Chow rings and Orlik--Solomon algebras, vastly generalizing a celebrated result of Getzler. This provides a new interpretation of combinatorial Leray models of Orlik--Solomon algebras.

Cited by

• Operads of moduli spaces of points in ℂ^d revisited
• Lie-operads and operadic modules from poset cohomology

Related

• Matroid complexes and Orlik-Solomon algebras
• Combinatorial and algebraic structure in Orlik-Solomon algebras
• An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits
• Distributive Laws and the Koszulness
• Operadic categories as a natural environment for Koszul duality