一类Filiform李代数的左对称代数结构

The Left Symmetric Algebraic Structure of a Class of Filiform Lie Algebras

本文运用导子和极大环面的定义,对一类特殊的filiform李代数进行了深入的探讨,并成功求得了这类特殊filiform李代数的一个极大环面,从而证明出这类filiform李代数满足左对称代数结构。这一发现不仅丰富了filiform李代数的理论体系,也为相关领域的研究提供了新的思路和方向。

In this paper, by using the definitions of derivation and maximal torus, a special class of filiform Lie algebras are discussed in depth, and a maximal torus of this special class of filiform Lie algebras is successfully obtained, which proves that this class of filiform Lie algebras satisfies the left symmetric algebraic structure. This finding not only enriches the theoretical system of filiform Lie algebras, but also provides new ideas and directions for research in related fields.