Ternary derivations of finite-dimensional real division algebras
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Universidad de La Rioja
info
ISSN: 0024-3795
Ano de publicación: 2007
Volume: 428
Número: 8
Páxinas: 2192-2219
Tipo: Artigo
Outras publicacións en: Linear Algebra and Its Applications
Resumo
We present for each n ∈ {1, 2, 4, 8} a group acting on the set of all division algebra structures on R n, and an invariant, the Lie algebra of ternary derivations, for this action. An exploration of these structures is conducted in terms of this new invariant obtaining simple descriptions of the division algebras involved. In the course of the investigation another family of algebras is considered, among them the algebra sl (4, F) of 4 × 4 traceless matrices with the symmetric product xy + yx - frac(1, 2) t (xy) I shows an exceptional behavior. © 2007 Elsevier Inc. All rights reserved.