Realizations of 3-Lie algebras

3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. In this paper, we provide a construction of 3-Lie algebras in terms of Lie algebras and certain linear functions. Moreover, with the construction from γ -matrices and two-dimensional extension...

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Veröffentlicht in:Journal of mathematical physics 2010-06, Vol.51 (6), p.063505-063505-12
Hauptverfasser: Bai, Ruipu, Bai, Chengming, Wang, Jinxiu
Format: Artikel
Sprache:eng
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Zusammenfassung:3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. In this paper, we provide a construction of 3-Lie algebras in terms of Lie algebras and certain linear functions. Moreover, with the construction from γ -matrices and two-dimensional extensions of metric Lie algebras, all the complex 3-Lie algebras in dimension ≤ 5 are obtained along this approach. As a special case, we study the structure of the 3-Lie algebras constructed from the general linear Lie algebras with trace forms and prove that they are semisimple and local.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3436555