English

Quadratic algebras with Ext algebras generated in two degrees

Rings and Algebras 2009-03-03 v1

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.

Keywords

Cite

@article{arxiv.0903.0344,
  title  = {Quadratic algebras with Ext algebras generated in two degrees},
  author = {Thomas Cassidy},
  journal= {arXiv preprint arXiv:0903.0344},
  year   = {2009}
}
R2 v1 2026-06-21T12:17:25.471Z