Rota-Baxter李$2$ -代数
Rota-Baxter Lie $2$-algebras
摘要：
本文引入Rota-Baxter李$2$ -代数的概念，它是Rota-Baxter李代数的一个范畴.证明了Rota-Baxter李$2$ -代数范畴与$2$ -项Rota-Baxter $L_\infty$ -代数范畴是等价的.引入了Rota-Baxter李代数的交叉模的概念，证明了严格$2$ -项Rota-Baxter $L_\infty$ -代数与Rota-Baxter李代数的交叉模之间存在一一对应.利用Rota-Baxter李代数的交叉模构造了李代数的交叉模.
英文摘要：
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.
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