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. At last, as applications of the crossed modules of Rota-Baxter Lie algebras, we give constructions of crossed modules of pre-Lie algebras and crossed modules of Lie algebras from them.
Keywords: Rota-Baxter Lie 2-algebra, 2-term Rota-Baxter L_\infty-algebra, crossed module
2020 MSC: 17B38, 18N25
Theory and Applications of Categories, Vol. 39, 2023, No. 19, pp 545-566.
Published 2023-05-30.
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