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 |
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Hauptverfasser: | , , |
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. |
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ISSN: | 0022-2488 1089-7658 |
DOI: | 10.1063/1.3436555 |