n-Lie代数的弱模与不变双线性型

Weak-modules of n-Lie Algebras and Invariant Bilinear Forms

定义了n_Lie代数的弱模及不变双线性型(定义1及定义2),讨论了n_Lie代数的模与Lie代数的模之间的关系,并且验证了n_Lie代数的模的对偶空间及张量积是n_Lie弱模,同时还并证明了n_Lie代数的不可约表示容许唯一的不变双线性型的条件(定理5及定理7).

The authors give the definitions of weak-module and invariant bilinear form for an n-Lie algebra, and prove that the dual spaces and tensor products of the module of an n-Lie algebra are weak modules. And also obtain that an non-degenerate irreducible representation admits a unique invariant bilinear form of an n-Lie algebra （Theorem5 and Theorem7）.