• Corpus ID: 237497477

# Lie theory and cohomology of relative Rota-Baxter operators

@inproceedings{Jiang2021LieTA,
title={Lie theory and cohomology of relative Rota-Baxter operators},
author={Jun Jiang and Yunhe Sheng and Chenchang Zhu},
year={2021}
}
• Published 4 August 2021
• Mathematics
A bstract . 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 di ﬀ erentiation…
2 Citations
• Y. Sheng
• Mathematics
Bulletin of the London Mathematical Society
• 2022
In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter ( RB$\mathsf {RB}$ ) Lie algebras, which have attracted quite much interest recently. Using Voronov's
• Mathematics
• 2022
Groups with various types of operators, in particular the recently introduced RotaBaxter groups, have generated renowned interest with close connections to numerical integrals, Yang-Baxter equation,

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A relative Rota–Baxter algebra is a triple ( A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev,
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A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of
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