反李三系的不变双线性型  

INVARIANT BILINEAR FORMS ON ANTI-LIE TRIPLE SYSTEMS

作　　者：张知学[1] 李华君[2] 董磊[3] 

机构地区：[1]河北大学数学系,河北保定071002 [2]保定师范专科学校数学系,河北保定071051 [3]河北农业大学理学院数学系,河北保定071001

出　　处：《数学年刊（A辑）》2004年第4期429-436,共8页Chinese Annals of Mathematics

摘　　要：本文考察了反李三系和它的标准嵌入李超代数的Killing型之间的关系,并且证明了反李三系的反对称不变双线性型可以被唯一地扩张到它的标准嵌入李超代数。作为扩张定理的一个应用,得到了二次李和反李三系的唯一分解定理。The authors investigate the relationship between the Killing form of an anti-Lie triple system and that of its standard imbedding Lie superalgebra, and prove that an invariant anti-symmetric bilinear form on an anti-Lie triple system can be uniquely extended to its standard imbedding Lie superalgebra. As an application of the extension theorem, finally, the unique decomposition theorems for the quadratic Lie and anti-Lie triple systems are obtained.

关 键 词：ε-李三系 李超代数 双线性型 

分 类 号：O152.5[理学—数学]