The triple cross product in \(\mathbb{R}^7\)
type: Item
instance of: scholarly article
title: The triple cross product in \(\mathbb{R}^7\)
zbMATH Open document ID: 0901.17003
DOI: 10.1016/S0034-4877(97)89756-X
published in: Reports on Mathematical Physics
publication date: 1998-01-07T00:00:00Z
review text: The authors consider the operation of the cross product on \(\mathbb{R}^7\) and its relations with the structures of Cayley numbers and Malcev algebras. Some identities and trace formulas are obtained. Using these, the authors describe the matrix representation of the smallest simple compact Lie algebra \({\mathcal G}_2\). It seems to the reviewer that essential parts of this paper are known to specialists on Lie algebras, for example, a close description of \({\mathcal G}_2\) can be found in [\textit{M. M. Postnikov}, `Lectures in geometry. Semester V: Lie groups and Lie algebras' (Russian) (Nauka, Moscow) (1982; Zbl 0597.22001)].
Mathematics Subject Classification ID: 17B25
zbMATH DE Number: 1091058
zbMATH Keywords: exceptional Lie algebras
zbMATH Keywords: cross product
zbMATH Keywords: matrix representation
zbMATH Keywords: simple compact Lie algebra \({\mathcal G}_2\)
author: Fátima Silva Leite
author: Peter E. Crouch
MaRDI profile type: Publication
cites work: Q3999262
cites work: Quark structure and octonions
cites work: Q3897665
cites work: Introduction to Lie Algebras and Representation Theory
cites work: Malcev Algebras
cites work: The geometry of hypercomplex matrices
full work available at URL: s0034-4877(97)89756-x
OpenAlex ID: W1989131109
description: scientific article; zbMATH DE number 1091058