论文标题
交换性匹配的rota-baxter操作员，带装饰的洗牌产品和匹配的Zinbiel代数
Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras
论文作者
论文摘要
Rota-baxter代数和洗牌产物都是由整体操作员和积分方程引起的代数结构。与简单的Riemann积分运算符为积分方程式提供了一个代数框架，免费的交换性Rota-baxter代数为代数框架提供了代数框架。 Zinbiel代数形成一个类别，其中shuffle产品代数是自由对象。由涉及多个积分运算符和内核的积分方程的代数结构的动机，我们研究了交换性匹配的rota-baxter代数，并构建了使用带有多种装饰的洗牌产品的自由对象。我们还在相对上下文中构建了自由匹配的rota-baxter代数，以模拟积分运算符对积分方程中系数函数的作用。我们最终表明，自由交换\匹配rota-baxter代数给出了自由匹配的Zinbiel代数，从而将Shuffle产品代数的表征推广为Loday获得的自由Zinbiel代数。
The Rota-Baxter algebra and the shuffle product are both algebraic structures arising from integral operators and integral equations. Free commutative Rota-Baxter algebras provide an algebraic framework for integral equations with the simple Riemann integral operator. The Zinbiel algebras form a category in which the shuffle product algebra is the free object. Motivated by algebraic structures underlying integral equations involving multiple integral operators and kernels, we study commutative matching Rota-Baxter algebras and construct the free objects making use of the shuffle product with multiple decorations. We also construct free commutative matching Rota-Baxter algebras in a relative context, to emulate the action of the integral operators on the coefficient functions in an integral equation. We finally show that free commutative \match Rota-Baxter algebras give the free matching Zinbiel algebra, generalizing the characterization of the shuffle product algebra as the free Zinbiel algebra obtained by Loday.
