李代数的张量积所确定的Leibniz代数

Leibniz algebras defined by tensor product of Lie algebras

讨论了李代数■以及由这个李代数诱导的Leibniz代数■的一些性质,主要从不变双线性型和导子看这两个代数之间的差异,证明了在特定条件下两者的不变双线性型维数是一致的.为进一步确定李代数■和■的差异,讨论了由■诱导的一类重要的李代数■;最后证明了,如果■是有限维半单李代数,■和■是同构的.

By the definition of Leibniz algebra,we showed thatG was a Leibniz algebra whenG was a Lie algebra.We also proved thatG andG have the same dimension of invariant symmetric bilinear forms in a special case,and the dimension of the derivation algebra ofG is always less than that ofG.G is one of the important Lie algebra induced byG,andG is isomorphic toG whenG is a finite dimensional semi-simple Lie algebra.