Koszul duality for quadratic algebras over a complex
type: Item
instance of: scholarly article
title: Koszul duality for quadratic algebras over a complex
zbMATH Open document ID: 0828.18004
author: Sergey Arkhipov
publication date: 1995-06-26T00:00:00Z
review text: The classical Koszul duality theorem states that the derived categories of graded modules over a quadratic Koszul algebra \(A\) and its dual \(A^!\) are equivalent provided that \(A^!\) is finite-dimensional. The author shows that a certain class of \(DGZ\)-algebras [\textit{A. A. Beilinson}, \textit{V. A. Ginsburg} and \textit{V. V. Schekhtman}, J. Geom. Phys. 5, No. 3, 317-350 (1988; Zbl 0695.14009)] possesses the same construction of the Koszul duality functor between the derived categories of \(DGZ\)-modules. Then the classical Koszul duality theorem is a easy consequence of this result.
reviewed by: Marek Golasiński
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 13D25
zbMATH DE Number: 767649
zbMATH Keywords: quadratic algebra
zbMATH Keywords: \(DG\)-module
zbMATH Keywords: \(DGZ\)-algebras
zbMATH Keywords: Koszul duality
zbMATH Keywords: derived categories
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 767649