Sweedler 4维Hopf代数的Rota-Baxter代数结构  

The Rota-Baxter Algebra Structures on Sweedler's 4-dimensional Hopf Algebra

作　　者：高凤霞[1,2] 杨士林 Feng Xia GAO;Shi LinYANG(College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China;Department of Basic Course,He'nan Institute of Technology,Xinxiang 453003,P.R.China)

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]河南工学院基础部,新乡453003

出　　处：《数学学报（中文版）》2019年第1期71-86,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671024;11471186);北京市自然科学基金资助项目(1162002)

摘　　要：设H_4是Sweedler4维Hopf代数.本文根据Rota-Baxter算子的定义和性质,建立H_4的权为λ的Rota-Baxter算子在选定基下的矩阵元素满足的二次方程组.通过求解权λ=0时的二次齐次方程组和权λ=1时的二次非齐次方程组,给出了Rota-Baxter算子相应的矩阵形式.Let H4 be the Sweedler’s 4-dimensional Hopf algebra. In this paper by the definition and property of Rota-Baxter operator, we establish the system of quadratic equations of the matrix elements of Rota-Baxter operators of H4 with weight A for a given base. By solving the system of the equations with weight λ = 0 and λ=1 the matrix forms of Rota-Baxter operators are given.

关 键 词：Sweedler代数 权 Rota-Baxter算子 

分 类 号：O151.21[理学—数学]