On Killing-Ricci forms of Lie triple algebras
On Killing-Ricci forms of Lie triple algebras
复制标题
论李三重代数的 Killing-Ricci 形式
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
M. Kikkawa
中科院分区：
文献类型：
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作者：
M. Kikkawa
作为李代数的Killing型和黎曼对称空间的切李三系的Ricci型的推广，引入了李三代数的KillingRicci形式的概念。对于一类李三代数($)，证明了如果它的Killing-Ricci形式是非退化的，则它被分解成单理想的直和。作为应用，研究了由半单李代数及其半单子代数组成的约化对的结构。
The notion of Killing-Ricci forms of Lie triple algebras is introduced as a generalization of both of Killing forms of Lie algebras and the Ricci forms of the tangent Lie triple systems of Riemannian symmetric spaces. For a class of Lie triple algebras ($, it is shown that ® is decomposed into a direct sum of simple ideals if its Killing-Ricci form is nondegenerate. As an application, structure of the reductive pair consisting of a semi-simple Lie algebra and its semi-simple subalgebra is investigated.