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Sweedler 4维Hopf代数的Rota-Baxter代数结构
引用本文:高凤霞,杨士林.Sweedler 4维Hopf代数的Rota-Baxter代数结构[J].数学学报,2019,62(1):71-86.
作者姓名:高凤霞  杨士林
作者单位: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
基金项目: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.


The Rota-Baxter Algebra Structures on Sweedler's 4-dimensional Hopf Algebra
Feng Xia GAO,Shi LinYANG.The Rota-Baxter Algebra Structures on Sweedler's 4-dimensional Hopf Algebra[J].Acta Mathematica Sinica,2019,62(1):71-86.
Authors:Feng Xia GAO  Shi LinYANG
Institution:1. College of Applied Sciences, Beijing University of Technology, Beijing 100124, P. R. China; 2. Department of Basic Course, He'nan Institute of Technology, Xinxiang 453003, P. R. China
Abstract: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 λ 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.Keywords Sweedler's algebra; weight; Rota-Baxter algebra
Keywords:Sweedler's algebra  weight  Rota-Baxter algebra  
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