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On Rota-Baxter Lie 2-algebras

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Shilong Zhang and Jiefeng Liu

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.

http://www.tac.mta.ca/tac/volumes/39/19/39-19.pdf

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