Koszul graded Möbius algebras and strongly chordal graphs

• Adam LaClair ^[1] ; Matthew Mastroeni ^[2] ; Jason McCullough ^[3] ; Irena Peeva ^[4]
  1. [1] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  2. [2] SUNY Polytechnic Institute

     SUNY Polytechnic Institute

     City of Utica, Estados Unidos

     
  3. [3] Iowa State University

     Iowa State University

     Township of Franklin, Estados Unidos

     
  4. [4] Cornell University

     Cornell University

     City of Ithaca, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 2, 2025
• Idioma: inglés
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• Resumen

  • 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.