Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras

  1. Madariaga Merino, Sara
  2. R. Bremner, Murray
  3. Benito Clavijo, María del Pilar
Linear and Multilinear Algebra

ISSN: 0308-1087

Year of publication: 2014

Type: Article

DOI: 10.1080/03081087.2014.930141 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Linear and Multilinear Algebra


Cited by

  • Scopus Cited by: 3 (12-01-2023)
  • Web of Science Cited by: 3 (30-12-2022)

JCR (Journal Impact Factor)

  • Year 2014
  • Journal Impact Factor: 0.738
  • Journal Impact Factor without self cites: 0.629
  • Article influence score: 0.46
  • Best Quartile: Q2
  • Area: MATHEMATICS Quartile: Q2 Rank in area: 103/312 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2014
  • SJR Journal Impact: 0.69
  • Best Quartile: Q2
  • Area: Algebra and Number Theory Quartile: Q2 Rank in area: 40/92

Scopus CiteScore

  • Year 2014
  • CiteScore of the Journal : 1.5
  • Area: Algebra and Number Theory Percentile: 69


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.