具有1-维导代数的6-维3-李代数的结构(英文)

Structures of six-Dim 3-Lie algebras with one-Dim derived algebras

3-李代数与数学及数学物理的很多领域有着密切的关系。研究6-维3-李代数的结构,对特征零域上导代数维数为1的6-维3-李代数L,研究L的内导子代数adL的结构及导子代数DerL的结构,给出每个内导子及导子的具体表达形式。讨论导代数维数为1的6-维3-李代数L的度量结构,证明特征零域上导代数维数为1的6-维3-李代数L不存在度量函数。

3 -Lie algebras have close relationships with the fields of mathematics and mathematical physics. Structures of six - dimensional 3 - Lie algebras are considered. For the six-dimensional 3 - Lie algebras L with dimL1 = 1 over a field of characteristic zero, the inner derivation algebras adL and deriva- tion algebras DerL are studied, and every derivation and inner derivation are provided concretely. The metric structures of the six-dimensional 3 - Lie algebras L with dimL1 = 1 are discussed, and it is proved that there does not exist metric structure on L.