论文标题
匹配的相对rota-baxter代数，匹配的树突形代数及其同一个
Matching relative Rota-Baxter algebras, matching dendriform algebras and their cohomologies
论文作者
论文摘要
Gao，Guo和Zhang [{\ em J.代数} 552（2020）134-170]最近引入了匹配的Rota-baxter代数的概念。匹配Rota-Baxter代数的概念将多个积分运算符与内核概括。同一位作者还引入了匹配的树突形代数作为匹配的rota-baxter代数的基础结构。在本文中，我们介绍了与匹配的树突状代数有关的相匹配的相对rota-baxter代数。我们定义了一个匹配的Yang-baxter方程，该方程会产生匹配的相对Rota-baxter代数。接下来，我们介绍了匹配的相对rota-baxter代数作为经典Hochschild共同体的副产品和由匹配操作员引起的新的共同体学的副产品。作为应用程序，我们表明我们的共同体控制着匹配的相对rota-baxter代数的形式变形理论。最后，我们使用多重非对称作业来定义匹配的树突状代数的共同体，并表明从匹配的相对rota-baxter代数的构造中存在形态学到诱导的匹配的树突状代数的共同体。我们通过考虑均匀匹配树突状代数来结束本文。
The notion of matching Rota-Baxter algebras was recently introduced by Gao, Guo and Zhang [{\em J. Algebra} 552 (2020) 134-170] motivated by the study of algebraic renormalization of regularity structures. The concept of matching Rota-Baxter algebras generalizes multiple integral operators with kernels. The same authors also introduced matching dendriform algebras as the underlying structure of matching Rota-Baxter algebras. In this paper, we introduce matching relative Rota-Baxter algebras that are also related to matching dendriform algebras. We define a matching associative Yang-Baxter equation whose solutions give rise to matching relative Rota-Baxter algebras. Next, we introduce the cohomology of a matching relative Rota-Baxter algebra as a byproduct of the classical Hochschild cohomology and a new cohomology induced by the matching operators. As an application, we show that our cohomology governs the formal deformation theory of the matching relative Rota-Baxter algebra. Finally, using multiplicative nonsymmetric operads, we define the cohomology of a matching dendriform algebra and show that there is a morphism from the cohomology of a matching relative Rota-Baxter algebra to the cohomology of the induced matching dendriform algebra. We end this paper by considering homotopy matching dendriform algebras.
