Rota-Baxter operators on 4-dimensional complex simple associative algebras
Rota-Baxter operators on 4-dimensional complex simple associative algebras
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DOI：
10.1016/j.amc.2013.12.032
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Xiaomin Tang;Yang Zhang;Q. Sun
中科院分区：
文献类型：
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作者：
Xiaomin Tang;Yang Zhang;Q. Sun
Rota-Baxter算子或关系被用来解决某些分析和组合问题，并被应用于数学和数学物理的许多领域。本文研究了4维复单结合代数上的权为零的Rota-Baxter算子，该代数同构于复数域上所有2× 2矩阵的代数.这类算子满足一般线性李代数gl 2（C）上的经典Yang-Baxter方程（的算子形式）.我们提供了两种不同的求解方法：一种是用手来展示解决大型非线性系统的技巧，另一种是用计算机代数来展示解决高维情况的可能性。
Rota–Baxter operators or relations were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. In this paper, we commence to study the Rota–Baxter operators of weight zero on a 4-dimensional complex simple associative algebra, which is isomorphic to the algebra of all 2× 2 matrices over the field of complex numbers. Such operators satisfy (the operator form of) the classical Yang–Baxter equation on the general linear Lie algebra gl 2 (C). We provide two different solving methods: one by hand to show some tricks for solving a large nonlinear system, and another one by Computer Algebra to show the possibility of solving higher dimensional cases.