G-Quadratic, LG-Quadratic, and Koszul Quotients of Exterior Algebras
Jason McCullough, Zachary Mere
TL;DR
This paper explores LG-quadratic quotients of exterior algebras, demonstrating their Koszul property, and provides examples distinguishing LG-quadratic, G-quadratic, and Koszul algebras, including the first noncommutative case.
Contribution
It introduces LG-quadratic quotients of exterior algebras, proves they are Koszul, and constructs novel examples differentiating between G-quadratic, LG-quadratic, and Koszul algebras.
Findings
LG-quadratic quotients of exterior algebras are Koszul
Constructed an LG-quadratic algebra that is not G-quadratic
Presented a Koszul algebra that is not LG-quadratic, first noncommutative example
Abstract
This paper introduces the study of LG-quadratic quotients of exterior algebras, showing that they are Koszul, as in the commutative case. We construct an example of an LG-quadratic algebra that is not G-quadratic and another example that is Koszul but not LG-quadratic. This is only the second known Koszul algebra that is not LG-quadratic and the first that is noncommutative.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Commutative Algebra and Its Applications