The Koszul dual of a weakly Koszul module

2007/02/02 by Dag Madsen, Madsen, Dag
Mathematics · #16S37 #16W50 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16S37 #msc:16W50 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0702054

20 pages

arxiv created 2007/02/02 · openalex publication_date 2007/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.

Related

• Properties of Koszul homology modules
• Detecting Koszulness and related homological properties from the algebra\n structure of Koszul homology
• Resolutions of Koszul complexes and applications
• Quasi-hereditary algebras and generalized Koszul duality
• On the regularity and Koszulness of modules over local rings