标题： 李括号在李代数的(右)双导子空间上的定义 显示英文标题

标题： A Lie Bracket on the Space of (Right) Biderivations of a Lie Algebra

摘要： 导子将微分的概念从函数扩展到满足莱布尼茨法则的代数结构中的线性算子。 在李代数中，导子通过线性自同态的换位子括号形成一个李代数。 受此启发，我们研究双导子——捕捉高阶无穷小对称性的双线性映射。 本工作聚焦于李代数的右双导子，引入双导子空间上的李括号以探索其代数和几何性质。 我们通过对称和反对称情况分析左双导子和右双导子括号之间的相互作用，提供了一个连贯的李代数框架。 此外，我们开始构建与双导子李代数对应的李群，连接无穷小和全局结构。 我们的结果为高阶导子提供了新的视角，潜在应用于形变理论和广义对称性研究。 显示英文摘要

摘要： Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms. Motivated by this, we study biderivations-bilinear maps capturing higher-order infinitesimal symmetries. This work focuses on right biderivations of Lie algebras, introducing Lie brackets on spaces of biderivations to explore their algebraic and geometric properties. We analyse the interplay between left and right biderivation brackets through symmetric and skew-symmetric cases, providing a coherent Lie algebra framework. Moreover, we initiate the construction of Lie groups corresponding to the Lie algebra of biderivations, linking infinitesimal and global structures. Our results offer new perspectives on higher-order derivations with potential applications in deformation theory and generalised symmetry studies.