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

    GRID grid.119021.a

  2. 2 University of Saskatchewan
    info

    University of Saskatchewan

    Saskatoon, Canadá

    GRID grid.25152.31

Journal:
Linear and Multilinear Algebra

ISSN: 0308-1087

Year of publication: 2015

Volume: 63

Issue: 6

Pages: 1257-1281

Type: Article

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

Metrics

Cited by

  • Scopus Cited by: 2 (14-07-2021)

Journal Citation Reports

  • Year 2015
  • Journal Impact Factor: 0.761
  • Best Quartile: Q2
  • Area: MATHEMATICS Quartile: Q2 Rank in area: 104/312 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2015
  • SJR Journal Impact: 0.582
  • Best Quartile: Q2
  • Area: Algebra and Number Theory Quartile: Q2 Rank in area: 41/91

CiteScore

  • Year 2015
  • CiteScore of the Journal : 1.3
  • Area: Algebra and Number Theory Percentile: 67

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.