Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals
Commutative Algebra
2016-06-22 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.0904.1683,
title = {Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals},
author = {Victor Reiner and Dumitru I. Stamate},
journal= {arXiv preprint arXiv:0904.1683},
year = {2016}
}
Comments
31 pages, 1 figure. Minor changes from previous version. To appear in Advances in Mathematics