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On Rota-Baxter Lie 2-algebras
Theory and applications of categories, Tome 39 (2023), pp. 545-566 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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.

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Classification : 17B38, 18N25
Keywords: Rota-Baxter Lie 2-algebra, 2-term Rota-Baxter L_\infty-algebra, crossed module 
@article{TAC_2023_39_a18,
     author = {Shilong Zhang and Jiefeng Liu},
     title = {On {Rota-Baxter} {Lie} 2-algebras},
     journal = {Theory and applications of categories},
     pages = {545--566},
     year = {2023},
     volume = {39},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a18/}
}
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Shilong Zhang; Jiefeng Liu. On Rota-Baxter Lie 2-algebras. Theory and applications of categories, Tome 39 (2023), pp. 545-566. http://geodesic.mathdoc.fr/item/TAC_2023_39_a18/