李代数的Rota-Baxter算子  

Rota-Baxter Operators of Lie Algebras

作　　者：范素军[1] 刘东艳[1] 吴艳茹[2] 崔丽娟[1] 

机构地区：[1]河北医科大学数学教研室,河北石家庄050017 [2]河北医科大学物理教研室,河北石家庄050017

出　　处：《河北师范大学学报（自然科学版）》2014年第6期541-544,共4页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金(A2007000138)

摘　　要：研究了复数域上导代数维数等于1的2-维和3-维李代数的Rota-Baxter算子的结构.给出了导代数维数等于1的2-维和3-维李代数的权为0的Rota-Baxter算子的具体表达式.并通过Rota-Baxter算子的可逆性讨论了李代数的幂零性.The Rota-Baxter operators have wide applications in mathematical physics.In this paper,we investigate the structure of Rota-Baxter operators on the two and three dimensional Lie algebras whose derived algebras are one dimensional.We give an explicit expression of every Rota-Baxter operator which has the weight zero,and also discuss the nilpotent property of Lie algebras by means of the reversibility of Rota-Baxter operators.

关 键 词：李代数 导代数 Rota-Baxter算子 

分 类 号：O152.5[理学—数学]