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Reiner, Victor; Stamate, Dumitru Ioan

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals. (English) Zbl 1266.16025

Adv. Math. 224, No. 6, 2312-2345 (2010).
Summary: We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.

Cited in 6 Documents

MSC:

16S37 Quadratic and Koszul algebras
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D02 Syzygies, resolutions, complexes and commutative rings
16S36 Ordinary and skew polynomial rings and semigroup rings
05E40 Combinatorial aspects of commutative algebra
06A11 Algebraic aspects of posets
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes

Keywords:

Koszul algebras; incidence algebras of posets; affine semigroup rings; linear resolutions; squarefree monomial ideals; sequential Cohen-Macaulay property

Software:

GAP
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Full Text: DOI arXiv

References:

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