Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras

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

ISSN: 0308-1087

Year of publication: 2014

Type: Article

Export: RIS
DOI: 10.1080/03081087.2014.930141 GOOGLE SCHOLAR lock_openOpen access editor

Metrics

Journal Citation Reports

  • Year 2014
  • Journal Impact Factor: 0.738
  • 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: 39/92

CiteScore

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

Abstract

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.