The indecomposable symplectic and quadratic modules of the Klein-four group
type: Item
instance of: scholarly article
title: The indecomposable symplectic and quadratic modules of the Klein-four group
zbMATH Open document ID: 1401.20020
author: Lars Pforte
author: John Murray
published in: Journal of Algebra
publication date: 2018-06-22T00:00:00Z
full work available at URL: JM maths the indecomposable.pdf
review text: Let \(G\) be the Klein \(4\)-group and \(k\) be a perfect field of characteristic \(2\). Since \(G\) has tame representation type, \(kG\) has only finitely many indecomposable modules of each dimension and these have been classified in [\textit{S. B. Conlon}, J. Aust. Math. Soc. 10, 363--366 (1969; Zbl 0186.04603)]. Using the notation of the latter paper, the \(kG\)-modules which give rise to indecomposable symplectic modules are: \((k_{G})^{2}\), \(kG\), \((kG)^{2}\), \(A_{n}\oplus B_{n}\), \(C_{n}(\pi)\), \(C_{n}(\pi)^{2}\), \(C_{n}(\infty)\) and \(C_{n}(\infty)^{2}\) where \(\pi\) is a monic irreducible polynomial over \(k\). For each of these \(kG\)-modules, the authors describe all symplectic forms, give representatives of the isometry classes of each form, and determine the \(G\)-invariant quadratic forms (if any) which polarize to the symplectic forms.
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 15A63
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 6893261
zbMATH Keywords: symplectic and quadratic forms
zbMATH Keywords: indecomposable symplectic and quadratic modules
zbMATH Keywords: Klein-four group
MaRDI profile type: Publication
OpenAlex ID: W2790301405
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Wikidata QID: Q130141600
DOI: 10.1016/J.JALGEBRA.2018.02.032
description: scientific article; zbMATH DE number 6893261