发表机构
School of Mathematics and Information Science, Guangzhou University（广州大学数学与信息科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带投影的双交叉积，证明其等价于Hopf代数上的相对Rota-Baxter算子，并探讨其与辫子算子及Doi-Hopf模态射的联系。
AI 中文摘要
给定一对匹配的Hopf代数，双交叉积构造产生一个新的Hopf代数，其典型例子是由（Hopf）斜配对产生的广义量子双代数。本文在Radford的双积理论框架下，专门研究带投影的双交叉积，并证明此类代数结构等价于Sciandra近期引入的Hopf代数上（Yetter-Drinfeld）相对Rota-Baxter算子的一种简化版本，相应的辫子Hopf代数在余伴随余作用下属于Yetter-Drinfeld模范畴。我们进一步考察该代数结构在单个Hopf代数上诱导匹配作用对的条件，这反过来等价于Hopf代数上产生辫子方程解的辫子算子的概念。此外，我们证明此类相对Rota-Baxter算子是某些Doi-Hopf模之间的态射。
英文摘要
Given a matched pair of Hopf algebras, the double cross product construction yields a new Hopf algebra, the prototypical example of which is the generalized quantum double arising from a (Hopf) skew pairing. In this paper, we specifically investigate double cross products with projections in the framework of Radford's biproduct theory, and establish that such an algebraic structure is equivalent to a simplified version of (Yetter-Drinfeld) relative Rota-Baxter operators on Hopf algebras recently introduced by Sciandra, with the corresponding braided Hopf algebras lying in the Yetter-Drinfeld module category under coadjoint coactions. We further examine conditions under which this algebraic structure induces a matched pair of actions on a single Hopf algebra, which is in turn equivalent to the notion of braiding operators on Hopf algebras that yield solutions of the braid equation. In addition, we show that such relative Rota-Baxter operators are morphisms between certain Doi-Hopf modules.
Comments19 pages
