李H-伪双代数的结合类比
An associative analogy of Lie H-pseudobialgebra
摘要：
本文研究了李H-伪双代数的结合类比--无穷小H-伪双代数。本文首先定义了无穷小H-伪双代数，并研究了这种新代数结构的一些性质。然后考虑无穷小H-伪双代数的子类--余边界无穷小H-伪双代数，得到了结合H-伪双代数上的结合杨-巴克斯特方程.最后，我们找到了（上边界）无穷小H-伪双代数与（上边界）李H-伪双代数之间的联系。同时，建立了H-伪代数上结合杨-巴克斯特方程与经典杨-巴克斯特方程之间的关系.
英文摘要：
The purpose of this paper is to study infinitesimal H-pseudobialgebra, which is an associative analogy of Lie H-pseudobialgebra. We first define the infinitesimal H-pseudobialgebra and investigate some properties of this new algebraic structure. Then we consider the coboundary infinitesimal H-pseudobialgebra, which is the subclass of infinitesimal H-pseudobialgebra and we obtain the associative Yang-Baxter equation over an associative H-pseudoalgebra. Finally, we found the connection between the (coboundary) infinitesimal H-pseudobialgebra and the (coboundary) Lie H-pseudobialgebra. Meanwhile, the relationship between the associative Yang-Baxter equation and the classical Yang-Baxter equation (over an H-pseudoalgebra) is established.
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