# 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} }

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

### A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras

- MathematicsBulletin 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…

### Operated groups, differential groups and Rota-Baxter groups with an emphasis on the free objects

- 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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