Matroid complexes and Orlik-Solomon algebras

Fuente: arXiv
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Main Author: Coron, Basile
Format: Preprint
Published: 2025
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author Coron, Basile
author_facet Coron, Basile
contents In this article we construct a combinatorial quasi-free differential graded model for the Orlik-Solomon algebra of supersolvable matroids, which generalizes in a matroidal setting the cdga of admissible graphs introduced by M. Kontsevich for the braid arrangements. Our construction draws on well-known concepts from matroid theory, including modularity, single-element extensions, and generalized parallel connections. We also show that this model carries a cooperadic structure in a suitably generalized sense. As an application, we use this model to give a new proof that the Orlik-Solomon algebras of supersolvable matroids are Koszul.
format Preprint
id arxiv_https___arxiv_org_abs_2506_15048
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Matroid complexes and Orlik-Solomon algebras
Coron, Basile
Combinatorics
Algebraic Topology
In this article we construct a combinatorial quasi-free differential graded model for the Orlik-Solomon algebra of supersolvable matroids, which generalizes in a matroidal setting the cdga of admissible graphs introduced by M. Kontsevich for the braid arrangements. Our construction draws on well-known concepts from matroid theory, including modularity, single-element extensions, and generalized parallel connections. We also show that this model carries a cooperadic structure in a suitably generalized sense. As an application, we use this model to give a new proof that the Orlik-Solomon algebras of supersolvable matroids are Koszul.
title Matroid complexes and Orlik-Solomon algebras
topic Combinatorics
Algebraic Topology
url https://arxiv.org/abs/2506.15048