A generalized Koszul theory and its application

Abstract

Let $A$ be a graded algebra. In this paper we develop a generalized Koszul theory by assuming that $A_0$ is self-injective instead of semisimple and generalize many classical results. The application of this generalized theory to directed categories and finite EI categories is described.

The revised version accepted by Tran. AMS

References in corpus (4)

• A Characterization of Finite EI Categories with Hereditary Category Algebras
• Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals
• Extension algebras of standard modules
• Algebras stratified for all linear orders

Cited by in corpus (10)

• Homological degrees of representations of categories with shift functors
• Koszulity of directed categories in representation stability theory
• Categorifications of rational Hilbert series and characters of $F{S}^{op}$ modules
• Algebras stratified for all linear orders
• Adjoint functors on the representation category of $\mathcal{OI}$
• The MCM-approximation of the trivial module over a category algebra
• PBW deformations of Koszul algebras over a nonsemisimple ring
• On compact exceptional objects in derived module categories
• Representations of Modular Skew Group Algebras
• The tensor product of Gorenstein-projective modules over category algebras