We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularity structures~[10,18]. This notion is also related to iterated integrals with multiple kernels and solutions of the associative polarized Yang-Baxter equation. Generalizing the natural connection of Rota-Baxter algebras with dendriform algebras to matching Rota-Baxter algebras , we obtain the notion of matching dendriform algebras. As in the classical case of one operation, matching Rota-Baxter algebras and matching dendriform algebras are related to matching pre-Lie algebras which coincide with the aforementioned multiple pre-Lie algebras. More general notions and results on matching tridendriform algebras and matching PostLie algebras are also obtained.

中文翻译：

---

匹配 Rota-Baxter 代数、匹配树状代数和匹配 pre-Lie 代数

我们引入了匹配 Rota-Baxter 代数的概念，这是由最近对正则结构代数重整化研究产生的多个 pre-Lie 代数的工作所激发的~[10,18]。这个概念也与具有多个核的迭代积分和关联极化 Yang-Baxter 方程的解有关。将 Rota-Baxter 代数与树状代数的自然联系推广到匹配 Rota-Baxter 代数，我们得到匹配树状代数的概念。与一个运算的经典情况一样，匹配 Rota-Baxter 代数和匹配树状代数与匹配与上述多个 pre-Lie 代数重合的 pre-Lie 代数有关。还获得了关于匹配三叉树形代数和匹配 PostLie 代数的更一般的概念和结果。