Filiform李代数Q_n的Hom-结构

The Hom-structures on Filiform Lie algebras Q_n

首先证明了有限维Z-阶化李代数上的一个线性算子是Hom-结构的充分必要条件,即它的每个齐次分支也是Hom-结构.然后计算了特征零代数闭域上一类有限维Z-阶化Filiform李代数Qn的齐次Hom-结构,从而决定了Qn的所有Hom-结构.

In this paper, we prove that a linear operator on a finite-dimensional Z-graded Lie algebra is a Horn-structure if and only if its homogeneous components are Hom-structures. We also compute homogeneous Horn-structures on a finite dimensional Z-graded Filiform Lie algebra Qn over an algebraically closed field of characteristic zero. As a consequence, we determine all the Hom-structures on Qn.