On triality and automorphisms and derivations of composition algebras
type: Item
instance of: scholarly article
title: On triality and automorphisms and derivations of composition algebras
zbMATH Open document ID: 1049.17003
DOI: 10.1016/S0024-3795(00)00105-1
author: Alberto Elduque
published in: Linear Algebra and its Applications
publication date: 2003-07-21T00:00:00Z
review text: Let \((C,q)\) be a Cayley-Dickson algebra over a field \(F\) of arbitrary characteristic with norm \(q\). The author studies automorphisms, derivations and orthogonal transformations of \((C,q)\) using the Principle of Triality for orthogonal transformations. He derives many new expressions for derivations and automorphisms. Also some well-known results are recovered. For example, it is shown as a corollary that all derivations of \(C\) are inner, and \(\dim_F \text{Der}\, C=14\). Furthermore, the Principle of Local Triality in arbitrary characteristic is proved for \(8\)-dimensional composition algebras.
reviewed by: Dietrich Burde
Mathematics Subject Classification ID: 17A75
Mathematics Subject Classification ID: 17A36
zbMATH DE Number: 1506620
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1506620