辛代数的不变双线性型  

Invariant Bilinear Forms on Symplectic Ternary Algebras

作　　者：白喜梅[1] 刘文丽[1] 张知学[1] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002

出　　处：《数学的实践与认识》2009年第5期174-179,共6页Mathematics in Practice and Theory

基　　金：河北省自然科学基金(A2005000088)

摘　　要：考察了辛代数和与它相联系的李三系的双线性型之间的关系,并证明了辛代数的反对称不变双线性型可以唯一扩张到与它相联系的李三系中.作为这种关系的一个应用,得到了二次辛代数是单辛代数的一个充要条件,并证明二次辛代数的唯一分解定理.The authors ,investigate the relationship between the form of a Symplectic ternary algebra and that of the Lie triple system associated with it, and prove that an invariant antisymmetric bilinear form on a Syrnmplectic ternary algebra can be uniquely extended to the Lie triple system associated with it. As an application of this relation, the authors prove that the dimension of （U ,b） is 1 if and only if U is simple. Finally, the unique decomposition theorem for the quandratic Symplectic ternary algebras is obtained.

关 键 词：辛代数 李三系 双线性型 

分 类 号：O152[理学—数学]