交换环上上三角矩阵李代数的李三次导子

Lie Triple Derivations of the Lie Algebra of Upper Triangular Matrice over Commutative Rings

为进一步研究导子,给出了李三次导子的概念,并利用其在矩阵基上的作用,将含有单位元的交换环上上三角矩阵李代数的任意一个李三次导子分解为内三次导子、中心三次导子之和,推广了导子的概念.

For the further study of derivations,the paper gives the concept of Li triple derivations and uses its effect in the matrix basis to decompose any triple derivation of Lie algebras of triangular matrices over commutative rings with unit elements into the sum of three inner derivations and the central three derivations,which generalizes the concept of derivations.