论文标题
相对rota-baxter Lie代数的变形和同义理论
Deformations and homotopy theory of relative Rota-Baxter Lie algebras
论文作者
论文摘要
我们确定\ emph {$ l_ \ infty $ -Algebra}控制一个相对rota-baxter的变形，并表明它是DG的延伸代数，控制了由DG Lie lie Algebra控制的lie algebra对相对Rota baxter ota baxter otator otator ota的lieerp lie liePer对的代数变形。因此，我们定义了相对rota-baxter的{\ em colomology}，并将其与它们的无限变形相关联。大量的相对Rota-baxter Lie代数是从三角形的双子骨中获得的，我们在相应的变形复合物之间构建图。接下来，引入了\ emph {同型}相对rota-baxter lie代数的概念。我们表明，一类同同处理相对rota-baxter lie代数与\ emph {pre-lie $ _ \ infty $ -algebras}密切相关。
We determine the \emph{$L_\infty$-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying LieRep pair by the dg Lie algebra controlling deformations of the relative Rota-Baxter operator. Consequently, we define the {\em cohomology} of relative Rota-Baxter Lie algebras and relate it to their infinitesimal deformations. A large class of relative Rota-Baxter Lie algebras is obtained from triangular Lie bialgebras and we construct a map between the corresponding deformation complexes. Next, the notion of a \emph{homotopy} relative Rota-Baxter Lie algebra is introduced. We show that a class of homotopy relative Rota-Baxter Lie algebras is intimately related to \emph{pre-Lie$_\infty$-algebras}.
