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Constructions of metric (n + 1)-Lie algebras

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Abstract

Metric n-Lie algebras have wide applications in mathematics and mathematical physics. In this paper, the authors introduce two methods to construct metric (n+1)-Lie algebras from metric n-Lie algebras for n ≥ 2. For a given m-dimensional metric n-Lie algebra (g, [, · · ·, ], B g ), via one and two dimensional extensions L = g +Fc and g0 = g + Fx −1 +Fx 0 of the vector space g and a certain linear function f on g, we construct (m+1)- and (m+2)-dimensional (n+1)-Lie algebras (L, [, · · ·, ] cf ) and (g0, [, · · ·, ]1), respectively. Furthermore, if the center Z(g) is non-isotropic, then we obtain metric (n+1)-Lie algebras (L, [, · · ·, ] cf , B) and (g0, [, · · ·, ]1, B) which satisfy B|g×g = B g . Following this approach the extensions of all (n + 2)-dimensional metric n-Lie algebras are discussed.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei University, Baoding, Hebei, 071002, China

    Ruipu Bai & Shuangshuang Chen

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  1. Ruipu Bai
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  2. Shuangshuang Chen
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Correspondence to Ruipu Bai.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11371245) and the Natural Science Foundation of Hebei Province (No.A2014201006).

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Bai, R., Chen, S. Constructions of metric (n + 1)-Lie algebras. Chin. Ann. Math. Ser. B 37, 729–742 (2016). https://doi.org/10.1007/s11401-016-0977-1

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  • DOI: https://doi.org/10.1007/s11401-016-0977-1

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