辛代数的不变双线性型

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.

Invariant Bilinear Forms on Symplectic Ternary Algebras

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 anti-symmetric bilinear form on a Symmplectic 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.