Koszul Graded M\'obius Algebras and Strongly Chordal Graphs

Autor:	LaClair, Adam, Mastroeni, Matthew, McCullough, Jason, Peeva, Irena
Rok vydání:	2024
Předmět:	Mathematics - Commutative Algebra Mathematics - Combinatorics Primary: 16S37 13E10 05B35 Secondary: 13P10 05E40 05C25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 28 pages, to appear in Selecta Mathematica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.18499 Zobrazit plný text záznamu View this record from Arxiv