Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras
- Benito, P. 1
- Bremner, M. 2
- Madariaga, S. 2
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1
Universidad de La Rioja
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2
University of Saskatchewan
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ISSN: 0308-1087
Year of publication: 2015
Volume: 63
Issue: 6
Pages: 1257-1281
Type: Article
More publications in: Linear and Multilinear Algebra
Metrics
JCR (Journal Impact Factor)
- Year 2015
- Journal Impact Factor: 0.761
- Journal Impact Factor without self cites: 0.595
- Article influence score: 0.486
- 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: 41/93
Scopus CiteScore
- Year 2015
- CiteScore of the Journal : 1.3
- Area: Algebra and Number Theory Percentile: 67
Related Projects
2014/00067/001
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.