李代数与一元扩张3-李代数的结构

Structures of Lie algebras and 1-ary extension 3-Lie algebras

研究李代数L与L的一元扩张3-李代数A的结构,给出内导子代数ad L与3-李代数A的内导子代数ad A之间的关系,证明李代数L的一元扩张3-李代数A的内导子代数ad A是ad L与一个Abel理想的半直积;利用2-立方阵,给出李代数的一元扩张3-李代数的实现。

Consider the structures of Lie algebra L and its 1-ary extension 3-Lie algebra A.The relation between the inner derivation algebra ad L and the inner derivation algebra ad A is given.And it is proved that the inner derivation algebra ad A of 1-ary extension 3-Lie algebra A is a semi-direct sum of ad L and an Abelian ideal.At last of the paper,an 1-ary extension 3-Lie algebra A is realized by 2-cubic matrices.