A duality theorem for generalized Koszul algebras

Abstract

We show that if $\Lambda$ is a $n$-Koszul algebra and $E=E(\Lambda)$ is its Yoneda algebra, then there is a full subcategory $\mathcal{L}_E$ of the category $Gr_E$ of graded $E$-modules, which contains all the graded $E$-modules presented in even degrees, that embeds fully faithfully into the category $C(Gr_\Lambda)$ of cochain complexes of graded $\Lambda$-modules. That extends the known equivalence, for $\Lambda$ Koszul (i.e. for $n=2$), between $Gr_E$ and the category of linear complexes of graded $\Lambda$-modules