Ternary derivations of finite-dimensional real division algebras

  1. Jiménez-Gestal, C. 1
  2. Pérez-Izquierdo, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Linear Algebra and Its Applications

ISSN: 0024-3795

Ano de publicación: 2007

Volume: 428

Número: 8

Páxinas: 2192-2219

Tipo: Artigo

DOI: 10.1016/J.LAA.2007.11.019 SCOPUS: 2-s2.0-39549098883 WoS: WOS:000254908900032 GOOGLE SCHOLAR

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.