Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras

  1. Benito, P. 1
  2. Bremner, M. 2
  3. Madariaga, S. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 University of Saskatchewan
    info

    University of Saskatchewan

    Saskatoon, Canadá

    ROR https://ror.org/010x8gc63

Revista:
Linear and Multilinear Algebra

ISSN: 0308-1087

Año de publicación: 2015

Volumen: 63

Número: 6

Páginas: 1257-1281

Tipo: Artículo

DOI: 10.1080/03081087.2014.930141 SCOPUS: 2-s2.0-84918796476 WoS: WOS:000346841800014 GOOGLE SCHOLAR

Otras publicaciones en: Linear and Multilinear Algebra

Resumen

On the set (Formula presented.) of symmetric (Formula presented.) matrices over the field (Formula presented.) , we can define various binary and ternary products which endow it with the structure of a Jordan algebra or a Lie or Jordan triple system. All these nonassociative structures have the orthogonal Lie algebra (Formula presented.) as derivation algebra. This gives an embedding (Formula presented.) for (Formula presented.). We obtain a sequence of reductive pairs (Formula presented.) that provides a family of irreducible Lie-Yamaguti algebras. In this paper, we explain in detail the construction of these Lie-Yamaguti algebras. In the cases (Formula presented.) , we use computer algebra to determine the polynomial identities of degree (Formula presented.) ; we also study the identities relating the bilinear Lie-Yamaguti product with the trilinear product obtained from the Jordan triple product.