Periodic resolutions over exterior algebras.
type: Item
instance of: scholarly article
title: Periodic resolutions over exterior algebras.
zbMATH Open document ID: 1081.13005
DOI: 10.1016/S0021-8693(02)00511-2
author: David Eisenbud
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: The author analyzes the structure of periodic modules over the exterior algebra \(E=\bigwedge V\) where \(V\) is a finite dimensional vector space over a field \(K\). A module \(M\) is called periodic if it is isomorphic to one of its syzygy modules \(\Omega_i(M)\) and the smallest index \(i\geq 1\) for which isomorphism occurs is called the period. It is shown that every module with bounded Betti numbers is periodic of period \(\leq 2\), and that the period is \(1\) if the module is graded. Moreover, a module with a linear Tate resolution is periodic of period \(1\). In the last part of the paper the author parametrizes the family of periodic modules over algebraically closed fields in terms of their representation matrices. A particularly nice description is obtained for graded periodic modules: In a sense, they are close to direct sums of quotients \(E/(a)\) where \(a\) is a linear form.
reviewed by: Winfried Bruns
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 16E05
Mathematics Subject Classification ID: 15A75
zbMATH DE Number: 1868092
zbMATH Keywords: exterior algebra
zbMATH Keywords: free resolutions
zbMATH Keywords: periodic resolution
describes a project that uses: Macaulay2
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1868092