Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras

Autor: Madariaga Merino, Sara; R. Bremner, Murray; Benito Clavijo, María del Pilar

Tipo de documento: Artículo de revista

Revista: Linear and Multilinear Algebra. ISSN: 0308-1087. Año: 2014.

doi 10.1080/03081087.2014.930141Texto completo open access 

Science  Área: MATHEMATICS  Quartil: Q2  Lugar área: 103/310  F. impacto: 0,738 

,675  SNIP: ,907 


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.