Constructions of Metric (n+1)-Lie Algebras  

作　　者：Ruipu BAI Shuangshuang CHEN 

机构地区：[1]College of Mathematics and Information Science, Hebei University

出　　处：《Chinese Annals of Mathematics,Series B》2016年第5期729-742,共14页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11371245);the Natural Science Foundation of Hebei Province(No.A2014201006)

摘　　要：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 ￡=g+IFc and g0= g+IFx^(-1)+IFx^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(￡, [, ···, ]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.

关 键 词：algebra extensions mathematics satisfy multiplication commutative degenerate Cartan bilinear isotropic 

分 类 号：O152.5[理学—数学]