n-Lie代数的半单准则(英文)

Criterion for Semisimplicity of an n-Lie Algebra

给出了n Lie代数的Killing型的非退化的定义 ,并证明了n Lie代数半单的的充要条件是它的Killing型是非退化的 .例证了一个半单的n Lie代数不一定分解为单理想的直和 .

The authors make a definition of non-degeneracy for the killing form of an n-Lie algebra and prove that an n-Lie algebra is semisimple if and only if its killing form is non-degenerate.The authors also give an example which shows that a semisimple n-Lie algebra need not to be a direct sum of simple ideals