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, [, · · ·, ], Bg), via one and two dimensional extensions L = g +Fc and g0 = g + Fx−1 +Fx0 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 = Bg. Following this approach the extensions of all (n + 2)-dimensional metric n-Lie algebras are discussed.
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