Ternary derivations of finite-dimensional real division algebras
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Universidad de La Rioja
info
ISSN: 0024-3795
Datum der Publikation: 2007
Ausgabe: 428
Nummer: 8
Seiten: 2192-2219
Art: Artikel
Andere Publikationen in: Linear Algebra and Its Applications
Zusammenfassung
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.