Some Results on Metric n-Lie Algebras

查看全文 作　　者：Rui Pu [1]BAI;Wan Qing [1]WU;Zhen Heng [2]LI

机构地区：[1]College of Mathematics and Computer Science,Hebei University;[2]Department of Mathematical Sciences,University of South Carolina Aiken

出　　处：《Acta Mathematica Sinica,English Series》索引2012年第28卷第6期,共12页

基　　金：Supported by National Natural Science Foundation of China (Grant No. 10871192);Natural Science Foundation of Hebei Province, China (Grant No. A2010000194) 摘　　要：We study the structure of a metric n-Lie algebra G over the complex field C. Let G = SR be the Levi decomposition, where R is the radical of G and S is a strong semisimple subalgebra of G. Denote by m(G) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R ⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R ⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to m(G) + 1. The centralizer of R in G is equal to the sum of all minimal ideals; it is the direct sum of R ⊥ and the center of G. Finally, G has no strong semisimple ideals if and only if R⊥■R. 关键词：N-LIE代数公制 Levi分解极小理想半单代数向量空间 N-李代数双线性形式

相关文献

参考文献（21）
引证文献（5）
耦合文献（0）

参考文献(21)

引证文献(5)

互联网出版许可证新出网证(渝)字10号全国400电话 - 免长途话费

Some Results on Metric n-Lie Algebras

参考文献(21)

引证文献(5)

用户提示