Non-Koszul quadratic Gorenstein toric rings
Kazunori Matsuda
TL;DR
This paper constructs a new example of a Gorenstein quadratic toric ring with socle degree greater than 3 that is not Koszul, expanding understanding of algebraic properties related to toric rings.
Contribution
It introduces a novel construction of non-Koszul Gorenstein quadratic toric rings with higher socle degree using stable set polytopes.
Findings
Constructed a non-Koszul Gorenstein quadratic toric ring with socle degree > 3
Demonstrated the existence of such rings using stable set polytopes
Extended the class of known Gorenstein quadratic toric rings
Abstract
Koszulness of Gorenstein quadratic algebras of small socle degree is studied. In this note, we construct non-Koszul Gorenstein quadratic toric ring such that its socle degree is more than 3 by using stable set polytopes.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics