论文标题
一项关于相对rota-baxter的变形，共同体和同义的调查
A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
论文作者
论文摘要
在本文中，我们回顾了相对rota-baxter lie代数的变形，共同体学和同义理论，这些理论最近引起了广泛的兴趣。使用Voronov的较高派生括号，可以获得$ L_ \ infty $ -Algebra，其Maurer-Cartan元素是相对Rota-Baxter lie代数。然后，使用扭曲方法，可以获得控制相对\ rb lie代数的变形的$ l_ \ infty $ algebra。同时，还可以在扭曲的$ l_ \ infty $ -Algebra的帮助下定义相对rota-baxter Lie代数的同族。使用控制代数方法，还可以介绍与pre lie $ _ \ infty $ -Algebras紧密连接的同型相对rota-baxter lie代数的概念。最后，我们简要审查了相对rota-baxter的变形，同型和同义理论，是非零重量的代数。
In this paper, we review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an $L_\infty$-algebra whose Maurer-Cartan elements are relative Rota-Baxter Lie algebras. Then using the twisting method, one can obtain the $L_\infty$-algebra that controls deformations of a relative \RB Lie algebra. Meanwhile, the cohomologies of relative Rota-Baxter Lie algebras can also be defined with the help of the twisted $L_\infty$-algebra. Using the controlling algebra approach, one can also introduce the notion of homotopy relative Rota-Baxter Lie algebras with close connection to pre-Lie$_\infty$-algebras. Finally, we briefly review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras of nonzero weights.
