标题： 有限维复单李代数上的相容根分级反前李代数结构 显示英文标题

标题： Compatible root graded anti-pre-Lie algebraic structures on finite-dimensional complex simple Lie algebras

摘要： 我们通过 ${\rm sl_2(\C)}$的表示理论来研究任何有限维复单李代数上的相容根分级反预-李代数结构。 我们证明除了 ${\rm sl_2(\C)}$外，有限维复单李代数上不存在相容根分级反预-李代数结构，而 ${\rm sl_2(\C)}$上恰好存在一个相容根分级反预-李代数结构。 显示英文摘要

摘要： We investigate the compatible root graded anti-pre-Lie algebraic structures on any finite-dimensional complex simple Lie algebra by the representation theory of ${\rm sl_2(\C)}$. We show that there does not exist a compatible root graded anti-pre-Lie algebraic structure on a finite-dimensional complex simple Lie algebra except ${\rm sl_2(\C)}$, whereas there is exactly one compatible root graded anti-pre-Lie algebraic structure on ${\rm sl_2(\C)}$.