Rota-Baxter Lie $2$-algebras
Category Theory
2022-03-08 v1
Abstract
In this paper, we introduce the notion of Rota-Baxter Lie -algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie -algebras and the category of -term Rota-Baxter -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 -term Rota-Baxter -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.
Cite
@article{arxiv.2203.03403,
title = {Rota-Baxter Lie $2$-algebras},
author = {Shilong Zhang and Jiefeng Liu},
journal= {arXiv preprint arXiv:2203.03403},
year = {2022}
}
Comments
19 pages. arXiv admin note: text overlap with arXiv:1403.2144 by other authors