Lie algebras generated by 3-forms
type: Item
instance of: scholarly article
title: Lie algebras generated by 3-forms
zbMATH Open document ID: 1148.17006
author: Rudolf Philippe Rohr
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2006-03-29T00:00:00Z
review text: Given a \(3\)-form \(T\) and an inner product \(B\) on a real vector space \(U\), on \(U\) there are a natural skew-form \([x,y]\) defined by the equality \(2 B([x,y],z) = T(x,y,z)\) and the mapping \(\sigma: U \to \text{so}(U,B) = \wedge^2 U^\ast\) given by the formula \(\sigma(x) = T(x,\cdot,\cdot)\). It is proved that this skew-form \([x,y]\) is a Lie bracket if and only if the image of \(\sigma\) is a Lie subalgebra of \(\text{so}(U,B)\).
reviewed by: I. A. Taimanov
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 5016280
zbMATH Keywords: Lie algebra
zbMATH Keywords: 3-form
Wikidata QID: Q57046197
MaRDI profile type: Publication
full work available at URL: j.crma.2006.01.006
OpenAlex ID: W2006348299
cites work: On the holonomy of connections with skew-symmetric torsion
cites work: Q5830680
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Q675876
DOI: 10.1016/J.CRMA.2006.01.006
description: scientific article; zbMATH DE number 5016280