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- W3201212711 abstract "In this paper, we establish a local Lie theory for relative Rota-Baxter operators of weight $1$. First we recall the category of relative Rota-Baxter operators of weight $1$ on Lie algebras and construct a cohomology theory for them. We use the second cohomology group to study infinitesimal deformations of relative Rota-Baxter operators and modified $r$-matrices. Then we introduce a cohomology theory of relative Rota-Baxter operators on a Lie group. We construct the differentiation functor from the category of relative Rota-Baxter operators on Lie groups to that on Lie algebras, and extend it to the cohomology level by proving the Van Est theorem between the two cohomology theories. We integrate a relative Rota-Baxter operator of weight 1 on a Lie algebra to a local relative Rota-Baxter operator on the corresponding Lie group, and show that the local integration and differentiation are adjoint to each other. Finally, we give two applications of our integration of Rota-Baxter operators: one is to give an explicit formula for the factorization problem, and the other is to provide an integration for matched pairs." @default.
- W3201212711 created "2021-09-27" @default.
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- W3201212711 date "2021-08-04" @default.
- W3201212711 modified "2023-10-16" @default.
- W3201212711 title "Lie theory and cohomology of relative Rota-Baxter operators" @default.
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- W3201212711 doi "https://doi.org/10.48550/arxiv.2108.02627" @default.
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