论文标题
$ 3 $ -Sop-post-Lie代数和非零重量的相对Rota-Baxter运算符$ 3 $ -LIE代数
$3$-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras
论文作者
论文摘要
在本文中，首先，我们介绍了$ 3 $ -lie代数和$ 3 $ -post-lie代数的非零重量的相对rota-baxter操作员的概念。一个3杆LIE代数由3-Lie代数结构和三元操作组成，因此满足了某些兼容条件。我们表明，非零重量的相对Rota-baxter操作员自然会诱导$ 3 $ post-lie代数。相反，一个$ 3 $的lie代数产生了一个新的3-lie代数，该代数称为SubataDhacent 3-lie代数，以及对原始3-Lie代数的动作。然后，我们构建了一个$ l_ \ infty $ -Algebra，其Maurer-Cartan元素是非零重量的相对Rota-baxter操作员。因此，我们获得了扭曲的$ l_ \ infty $ -Algebra，该代数控制了给定的相对Rota-baxter在3-lie代数上的非零重量的变形。最后，我们为非零重量的相对Rota-baxter操作员介绍了一个同时理论，以$ 3 $ -LIE代数为代数，并使用第二个共同体学组对无限变形进行了分类。
In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on $3$-Lie algebras and $3$-post-Lie algebras. A 3-post-Lie algebra consists of a 3-Lie algebra structure and a ternary operation such that some compatibility conditions are satisfied. We show that a relative Rota-Baxter operator of nonzero weight induces a $3$-post-Lie algebra naturally. Conversely, a $3$-post-Lie algebra gives rise to a new 3-Lie algebra, which is called the subadjacent 3-Lie algebra, and an action on the original 3-Lie algebra. Then we construct an $L_\infty$-algebra whose Maurer-Cartan elements are relative Rota-Baxter operators of nonzero weight. Consequently, we obtain the twisted $L_\infty$-algebra that controls deformations of a given relative Rota-Baxter operator of nonzero weight on 3-Lie algebras. Finally, we introduce a cohomology theory for a relative Rota-Baxter operator of nonzero weight on $3$-Lie algebras and use the second cohomology group to classify infinitesimal deformations.
