Alternating multilinear forms
type: Item
instance of: scholarly article
title: Alternating multilinear forms
zbMATH Open document ID: 0831.15017
author: Lemnouar Noui
author: Philippe Revoy
published in: Annales Mathématiques Blaise Pascal
publication date: 1996-02-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79104
review text: Let \(E\) be a finite dimensional \(K\)-vector space. The authors study the action of the linear group \(GL (E)\) on the space \(\Lambda^p E\). As \(\Lambda^p E^* \cong (\Lambda^pE)^*\), there is no difference between alternating forms and \(p\)-vectors. Some authors have studied the case \(p = 3\) and \(\dim E \leq 9\), over an algebraically closed field in the general case. The present authors are still interested in the case \(n = 7\), they talk about invariants of arithmetical, algebraic and geometric meaning that one may assign to a \(p\)-vector. Then they apply this to the cases \(n = 6\), \(n = 7\) giving a complete analysis of the situation. Moreover they give a complete proof of Schouten's classification for \(n = 3\), \(n = 7\) and algebraically closed \(K\) and a precise description for the finite fields case.
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 784555
zbMATH Keywords: vector space
zbMATH Keywords: \(p\)-vectors
zbMATH Keywords: linear group
zbMATH Keywords: alternating forms
zbMATH Keywords: Schouten's classification
zbMATH Keywords: finite fields
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
OpenAlex ID: W2323751738
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DOI: 10.5802/AMBP.12
description: scientific article; zbMATH DE number 784555