Sweedler 4维Hopf代数的Rota-Baxter代数结构

高凤霞, 杨士林

数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 71-86.

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PDF(449 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (1) : 71-86. DOI: 10.12386/A2019sxxb0007
论文

Sweedler 4维Hopf代数的Rota-Baxter代数结构

    高凤霞1,2, 杨士林1
作者信息 +

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

    Feng Xia GAO1,2, Shi LinYANG1
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文章历史 +

摘要

设H4是Sweedler4维Hopf代数.本文根据Rota-Baxter算子的定义和性质,建立H4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.

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

关键词

Sweedler代数 / / Rota-Baxter算子

Key words

Sweedler's algebra / weight / Rota-Baxter algebra

引用本文

导出引用
高凤霞, 杨士林. Sweedler 4维Hopf代数的Rota-Baxter代数结构. 数学学报, 2019, 62(1): 71-86 https://doi.org/10.12386/A2019sxxb0007
Feng Xia GAO, Shi LinYANG. The Rota-Baxter Algebra Structures on Sweedler's 4-dimensional Hopf Algebra. Acta Mathematica Sinica, Chinese Series, 2019, 62(1): 71-86 https://doi.org/10.12386/A2019sxxb0007

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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)

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