Symmetric composition algebras
type: Item
instance of: scholarly article
title: Symmetric composition algebras
zbMATH Open document ID: 0904.17004
author: Alberto Elduque
published in: Journal of Algebra
publication date: 1999-01-21T00:00:00Z
review text: A composition algebra \(A\) over a field \(F\) is called symmetric if its norm \(n\) is associative, i.e. it satisfies \(n(xy,z)= n(x,yz)\) for any \(x,y,z\in A\). One important class of symmetric composition algebras are the Okubo algebras, which are the forms of the pseudo-octonion algebra. In the introduction the author summarizes the classification of the composition algebras over fields of characteristic not equalling 3. Then he tackles the classification of the Okubo algebras over fields of characteristic 3. As a first step, he gives a new construction of some Okubo algebras \(C_{\lambda,\mu}\) depending on two parameters \(\lambda,\mu\in F\). Next the author shows that for any Okubo algebra \(A\) without nonzero idempotents there are suitable \(\lambda,\mu\in F\) such that \(A\) is isomorphic to \(C_{\lambda,\mu}\). Finally he provides the classification of the symmetric composition algebras over fields of characteristic 3. Thus the classification of the symmetric composition algebras is complete.
reviewed by: Huberta Lausch
Mathematics Subject Classification ID: 17A75
zbMATH DE Number: 1089124
zbMATH Keywords: symmetric algebra
zbMATH Keywords: composition algebra
zbMATH Keywords: Okubo algebras
MaRDI profile type: Publication
full work available at URL: jabr.1997.7071
OpenAlex ID: W2008484835
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DOI: 10.1006/JABR.1997.7071
description: scientific article; zbMATH DE number 1089124