论文标题
$ l_ \ iftty $ - 联想性rota-baxter代数和同型rota-baxter操作员
The $L_\infty$-deformations of associative Rota-Baxter algebras and homotopy Rota-Baxter operators
论文作者
论文摘要
相对rota-baxter代数是由代数$ a $，$ a $ a-bimodule $ m $和相对rota-baxter运算符$ t $组成的三重$（a，m，t）$。使用Voronov的衍生支架和Lazarev等人的最新作品，我们构建了一个$ L_ \ Infty [1] $ - 代数，其Maurer-Cartan元素是相对相对的Rota-Baxter代数。通过标准扭曲，我们定义了一个新的$ l_ \ infty [1] $ - 代数，该代数控制着相对rota-baxter代数$（a，m，t）$的毛勒 - 卡丹变形。我们介绍了相对Rota-baxter代数$（A，M，T）$的共同体，并根据此共同体学（低维度）进行了研究无限变形。作为一种应用，我们推断出耦合偏斜的无限双ge骨的共同体学，并讨论它们的无限变形。最后，我们定义了同型相对rota-baxter操作员，并找到与同型树突状代数和同型代数的关系。
A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an $L_\infty [1]$-algebra whose Maurer-Cartan elements are precisely relative Rota-Baxter algebras. By a standard twisting, we define a new $L_\infty [1]$-algebra that controls Maurer-Cartan deformations of a relative Rota-Baxter algebra $(A,M,T)$. We introduce the cohomology of a relative Rota-Baxter algebra $(A, M, T)$ and study infinitesimal deformations in terms of this cohomology (in low dimensions). As an application, we deduce cohomology of coboundary skew-symmetric infinitesimal bialgebras and discuss their infinitesimal deformations. Finally, we define homotopy relative Rota-Baxter operators and find their relationship with homotopy dendriform algebras and homotopy pre-Lie algebras.
