论文标题
hopf后代数，相对rota-baxter操作员和杨巴克斯特方程的解决方案
Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
论文作者
论文摘要
在本文中，首先，我们介绍了HOPF后代数的概念，该代数在原始元素的空间上引起了lie后代数，并且自然存在于lie后代数的通用包围代数上的hopf后代数结构。一种新颖的特性是，同时性的HOPF后代数产生了广义的Grossman-Larsson产品，该产品导致了亚adjacent Hopf代数，可用于构建Yang-Baxter方程的解决方案。然后，我们在HOPF代数上介绍了相对Rota-Baxter操作员的概念。同时性的HOPF后代数产生了其子粘结型HOPF代数上的相对Rota-baxter操作员。相反，相对的旋转式运算符还诱导了HOPF后代数。然后，我们表明相对旋转式运算符会产生匹配的HOPF代数对。因此，HOPF后代数和相对Rota-baxter操作员在某些共同互动的HOPF代数中提供了Yang-Baxter方程的解决方案。最后，我们使用相对的rota-baxter操作员在原始元素，图形和模块bialgebra结构上使用相对的rota-baxter操作员在HOPF代数上表征相对的Rota-baxter操作员。
In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larsson product, which leads to a subadjacent Hopf algebra and can be used to construct solutions of the Yang-Baxter equation. Then we introduce the notion of relative Rota-Baxter operators on Hopf algebras. A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra. Conversely, a relative Rota-Baxter operator also induces a post-Hopf algebra. Then we show that relative Rota-Baxter operators give rise to matched pairs of Hopf algebras. Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions of the Yang-Baxter equation in certain cocommutative Hopf algebras. Finally we characterize relative Rota-Baxter operators on Hopf algebras using relative Rota-Baxter operators on the Lie algebra of primitive elements, graphs and module bialgebra structures.
