论文标题
二链3-lie代数，全面匹配的3 lie代数和O-操作员
Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators
论文作者
论文摘要
在本文中，首先，我们介绍了一个斜纹3 lie代数的概念，并构建了一个$ l_ \ infty $ - 代数，其Maurer-Cartan元素通过扭曲产生了新的Twill 3-Lie代数。特别是，我们恢复了3 $ - 代数的谎言$ 3 $ - 代数，其毛勒 - 卡丹元素是3-lie代数上的o-operators（也称为相对rota-baxter操作员）。然后，我们使用3-lie代数的广义表示，介绍了一对3-lie代数的广义匹配对的概念，这将产生二链3-lie代数。通常匹配的3个lie代数对应于特殊的二链3 lie代数类，我们称之为严格的斜纹三个lie代数。最后，我们使用O-操作员来构建显式二链三lie代数，并解释为什么3卢比代数的$ r $ -matrix无法引起双重构造3-lie bialgebra。给出了二链3 lie代数的示例，以说明各种有趣的现象。
In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an $L_\infty$-algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras by twisting. In particular, we recover the Lie $3$-algebra whose Maurer-Cartan elements are O-operators (also called relative Rota-Baxter operators) on 3-Lie algebras. Then we introduce the notion of generalized matched pairs of 3-Lie algebras using generalized representations of 3-Lie algebras, which will give rise to twilled 3-Lie algebras. The usual matched pairs of 3-Lie algebras correspond to a special class of twilled 3-Lie algebras, which we call strict twilled 3-Lie algebras. Finally, we use O-operators to construct explicit twilled 3-Lie algebras, and explain why an $r$-matrix for a 3-Lie algebra can not give rise to a double construction 3-Lie bialgebra. Examples of twilled 3-Lie algebras are given to illustrate the various interesting phenomenon.
