METRIC n-LIE ALGEBRAS

被引：4

作者：

Jin, Yidong ^{[2
]}

Liu, Wenli ^{[1
]}

Zhang, Zhixue ^{[1
]}

机构：

[1] Hebei Univ, Coll Math & Comp, Baoding 071002, Hebei, Peoples R China

[2] N China Elect Power Univ, Sch Math & Phys, Baoding, Hebei, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2011年 / 39卷 / 02期

关键词：

Invariant scalar product; n-Lie algebra; Metric n-Lie algebra; BILINEAR-FORMS; TRIPLE-SYSTEMS;

D O I：

10.1080/00927871003596198

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An n-Lie algebra is said to be metric if it is endowed with an invariant, non-degenerate, symmetric bilinear form. We prove that any simple n-Lie algebra over an algebraically closed field of characteristic zero admits a unique metric structure and vice versa. Further, we present two metric n-Lie algebras, which are indecomposable but admit many more metric structures.

引用

页码：572 / 583

页数：12

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