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<p>The graded Möbius 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 Möbius algebras are Koszul. We characterize the Koszul graded Möbius 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.</p>

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Koszul graded Möbius algebras and strongly chordal graphs

  • 期刊论文

  • 发表日期：

    2025年3月5日

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  • Adam LaClair,
  • Matthew Mastroeni,
  • Jason McCullough,
  • Irena Peeva

摘要

The graded Möbius 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 Möbius algebras are Koszul. We characterize the Koszul graded Möbius 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.