Koszul Graded M\"obius Algebras and Strongly Chordal Graphs
Commutative Algebra
2024-12-25 v1 Combinatorics
Abstract
The graded M\"{o}bius algebra of a matroid is a commutative graded algebra which encodes the combinatorics of the lattice of flats of the matroid. As a special subalgebra of the augmented Chow ring of the matroid, it plays an important role in the recent proof of the Dowling-Wilson Top Heavy Conjecture. Recently, Mastroeni and McCullough proved that the Chow ring and the augmented Chow ring of a matroid are Koszul. We study when graded M\"obius algebras are Koszul. We characterize the Koszul graded M\"obius algebras of cycle matroids of graphs in terms of properties of the graphs. Our results yield a new characterization of strongly chordal graphs via edge orderings.
Cite
@article{arxiv.2412.18499,
title = {Koszul Graded M\"obius Algebras and Strongly Chordal Graphs},
author = {Adam LaClair and Matthew Mastroeni and Jason McCullough and Irena Peeva},
journal= {arXiv preprint arXiv:2412.18499},
year = {2024}
}
Comments
28 pages, to appear in Selecta Mathematica