论文标题
Rota-baxter系统和偏斜桁架
Rota-Baxter systems and skew trusses
论文作者
论文摘要
作为偏斜括号的概括，T。Brzezinski引入了偏斜桁架的概念。结果表明，每个Rota-baxter群都有V. G. Bardakov和V. Gubarev的偏斜支撑的结构。为了研究具有偏斜桁架结构的Rota-baxter组的类似物，我们定义了Rotabaxter系统。我们研究了旋转式控制器系统与旋转式驱动器组之间的关系。此外，我们证明Rota-baxter系统可以分解为两个半群的直接总和。事实证明了分解定理，从而推广了Rota-Baxter组的分解定理。引入了lie代数的Rota-baxter系统的概念，作为Rota-Baxter Lie代数的概括。研究了Lie代数的Rota-Baxter系统与谎言组之间的联系。最后，作为修改后的杨巴克斯特方程的概括，我们定义了扭曲的修改后的杨巴克斯特方程。我们通过Lie代数的Rota-baxter系统提供了扭曲的修饰的Yang-Baxter方程的解决方案。
As a generalization of skew braces, the notion of skew trusses was introduced by T. Brzezinski. It was shown that every Rota-Baxter group has the structure of skew braces by V. G. Bardakov and V. Gubarev. To investigate an analogue of Rota-Baxter groups which has the structure of skew trusses, we define RotaBaxter systems. We study the relationship between Rota-Baxter systems and Rota-Baxter groups. Furthermore, we prove that a Rota-Baxter system can be decomposed as a direct sum of two semigroups. A factorization theorem is proved, generalizing the factorization theorem of Rota-Baxter groups. The notion of Rota-Baxter systems of Lie algebras was introduced, as a generalization of Rota-Baxter Lie algebras. The connection between Rota-Baxter systems of Lie algebras and Lie groups is studied. Finally, as a generalization of the modified Yang-Baxter equation, we define twisted modified Yang-Baxter equations. We give solutions of twisted modified Yang-Baxter equations by Rota-Baxter systems of Lie algebras.
