论文标题
rota-baxter谎言$ 2 $ - 代数
Rota-Baxter Lie $2$-algebras
论文作者
论文摘要
在本文中，我们介绍了Rota-Baxter Lie的概念$ 2 $ - 代数，这是Rota-Baxter Lie代数的分类。我们证明，rota-baxter的类别$ 2 $ - 代数和$ 2 $ -Term rota-baxter $ l_ \ infty $ -algebras的类别是等效的。我们介绍了rota-baxter lie代数的交叉模块的概念，并表明严格的2 $ 2 $ - term rota-baxter $ l_ \ infty $ -Algebras和rota-baxter lie代数的交叉模块之间存在一对一的对应关系。我们从rota-baxter lie代数的交叉模块中构建了lie代数的交叉模块。
In this paper, we introduce the notion of Rota-Baxter Lie $2$-algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie $2$-algebras and the category of $2$-term Rota-Baxter $L_\infty$-algebras are equivalent. We introduce the notion of a crossed module of Rota-Baxter Lie algebras and show that there is a one-to-one correspondence between strict $2$-term Rota-Baxter $L_\infty$-algebras and crossed modules of Rota-Baxter Lie algebras. We give the construction of crossed modules of Lie algebras from crossed modules of Rota-Baxter Lie algebras.
