δJordan-李三系上带有权λ的k-阶广义导子  

K-ORDER GENERALIZED DERIVATIONS OF WEIGHTλONδJORDAN-LIE TRIPLE SYSTEMS

作　　者：刘宁 张庆成[2] LIU Ning;ZHANG Qing-cheng(School of Mathematics,South China University of Technology,Guangzhou 510604,China;School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China)

机构地区：[1]华南理工大学数学学院,广东广州510604 [2]东北师范大学数学与统计学院,吉林长春130024

出　　处：《数学杂志》2021年第1期37-56,共20页Journal of Mathematics

基　　金：Supported by NSFC(11471090);NSFJL(20130101068JC)

摘　　要：本文研究了δJordan-李三系上带有权λ的k-阶广义导子的相关问题.通过计算,得到了每一个δJordan-李三系上带有权λ的k-阶Jordan三角θ-导子都是一个带有权λ的k-阶θ-导子.在定义下,给出了带有权λ的k-阶Jordan三角θ-导子的另一种等价形式.同时,建立了带有权λ的k-阶广义(θ,ϕ)-导子和Rota-BaxterδJordan-李三系上带有权λ的Rota-Baxter算子的遗传性质,得到了每一个Rota-BaxterδJordan-李代数能看成一个Rota-BaxterδJordan-李三系的结论.This paper deals with the k-order generalized derivations of weight λ on δ JordanLie triple systems. By computing, we conclude that every k-order Jordan triple θ-derivation of weight λ on δ Jordan-Lie triple systems is a k-order θ-derivation of weight λ. Under the definitions,we give another equivalent form of k-order Jordan triple θ-derivation of weight λ. Meanwhile,We also establish the inheritance property of k-order generalized(θ,φ)-derivation of weight λ and Rota-Baxter operator of weight λ on Rota-Baxter δ Jordan-Lie triple systems. We obtain that every Rota-Baxter δ Jordan-Lie algebra can be seen as a Rota-Baxter δ Jordan-Lie triple system.

关 键 词：δJordan-李三系 k-阶(θ ϕ)-导子 k-阶Jordan三角(θ ϕ)-导子 权λ 权λ的Rota-BaxterδJordan-李三系 

分 类 号：O152.5[理学—基础数学]