论文标题
Rota-Baxter家族代数的变形和同义理论
Deformations and homotopy theory for Rota-Baxter family algebras
论文作者
论文摘要
Rota-Baxter家族代数的概念是Rota-Baxter代数的概括。它自然出现在量子场理论重新归当的代数方面。 Rota-Baxter家族代数与树突状系列代数密切相关。在本文中，我们首先构建了一个$ l_ \ infty $ -Algebra，其Maurer-Cartan元素对应于Rota-Baxter家族代数结构。使用这种表征，我们定义了给定的Rota-baxter家族代数的共同体。为了应用我们的共同体学，我们研究了给定的rota-baxter家族代数的形式和无穷小变形。接下来，我们在给定的$ a_ \ infty $ -Algebra上定义了同型rota-baxter家族代数结构的概念。我们通过考虑Dendriform家族代数的同型版本及其与同型Rota-Baxter家族代数的关系结束本文。
The concept of Rota-Baxter family algebra is a generalization of Rota-Baxter algebra. It appears naturally in the algebraic aspects of renormalizations in quantum field theory. Rota-Baxter family algebras are closely related to dendriform family algebras. In this paper, we first construct an $L_\infty$-algebra whose Maurer-Cartan elements correspond to Rota-Baxter family algebra structures. Using this characterization, we define the cohomology of a given Rota-Baxter family algebra. As an application of our cohomology, we study formal and infinitesimal deformations of a given Rota-Baxter family algebra. Next, we define the notion of a homotopy Rota-Baxter family algebra structure on a given $A_\infty$-algebra. We end this paper by considering the homotopy version of dendriform family algebras and their relations with homotopy Rota-Baxter family algebras.
