Quadratic algebras with Ext algebras generated in two degrees
Thomas Cassidy

TL;DR
This paper constructs non-Koszul quadratic algebras that mimic Koszul properties up to any finite cohomological degree, providing new examples that challenge existing classifications.
Contribution
It introduces explicit non-commutative quadratic algebras with bigraded Yoneda algebras generated in two specific degrees, answering a question by Green and Marcos.
Findings
Existence of non-Koszul algebras appearing Koszul up to any degree
Construction of algebras with Yoneda algebra generated in degrees (1,1) and (m,m+1)
Examples of m-Koszul algebras that are not Koszul
Abstract
We show that there exist non-Koszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m>2 we exhibit a non-commutative quadratic algebra for which the corresponding bigraded Yoneda algebra is generated in degrees (1,1) and (m,m+1). The algebra is therefore not Koszul but is m-Koszul (in the sense of Backelin). These examples answer a question of Green and Marcos.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Commutative Algebra and Its Applications
