Dualities in Koszul graded AS Gorenstein algebras

2012/11/05 by Roberto Martínez-Villa, Martinez-Villa, Roberto
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1211.0945

openalex publication_date 2012/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is dedicated to the study of certain non commutative graded AS Gorenstein algebras Λ. The main result of the paper is that for Koszul algebras Λ with Yoneda algebra Γ, such that both Λ and Γ are graded AS Gorenstein noetherian of finite local cohomology dimension on both sides, there are dualities of triangulated categories: \underlinegr_Λ[Ω^-1] ≅ D^b(Qgr_Γ) and \underlinegr_Γ[Ω^-1] ≅ D^b(Qgr_Λ) where, and Qgr_Γ is the category of tails, this is: the category of finitely generated graded modules gr_Γ divided by the modules of finite length, and D^b(Qgr_Γ) the corresponding derived category and \underlinegr_Λ[Ω^-1] the stabilization of the category of finetely generated graded Λ-modules, module the finetely generated projective modules.

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