标题： Rota-Baxter算子的L-R smash乘积构造 显示英文标题

标题： Constructions of Rota-Baxter operators by L-R smash products

摘要： 设$A$和$H$为两个余交换的霍普夫代数，使得$A$是一个$H$-双模霍普夫代数。 假设$R:A\rightarrow A$是一个线性映射，$B$是$H$的罗塔-巴克斯特算子。 在本文中，我们将表征L-R平展积$A\natural H$上的Rota-Baxter算子，并给出使$\overline{B}$成为$A\natural H$的Rota-Baxter算子的充分必要条件。 然后我们将考虑对偶情况，并在 L-R 拓扑余积 $C\ltimes H$上构造一个 Rota-Baxter 余算子，其中 $C$ 和 $H$是交换的 Hopf 代数，而 $C$是一个 $H$-双模 Hopf 代数。 显示英文摘要

摘要： Let $A$ and $H$ be two cocommutative Hopf algebras such that $A$ is an $H$-bimodule Hopf algebra. Suppose that $R:A\rightarrow A$ is a linear map and $B$ is a Rota-Baxter operator of $H$. In this paper we will characterize the Rota-Baxter operators on the L-R smash product $A\natural H$ and give the necessary and sufficient conditions to make $\overline{B}$ a Rota-Baxter operator of $A\natural H$. Then we will consider the dual case, and construct a Rota-Baxter co-operator on the L-R smash coproduct $C\ltimes H$, where $C$ and $H$ are commutative Hopf algebras and $C$ is an $H$-bicomodule Hopf algebra.