• Corpus ID: 237497477

Lie theory and cohomology of relative Rota-Baxter operators

  title={Lie theory and cohomology of relative Rota-Baxter operators},
  author={Jun Jiang and Yunhe Sheng and Chenchang Zhu},
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

  • 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

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

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,



Integration and geometrization of Rota-Baxter Lie algebras

The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators

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,

Rota-Baxter operators on cocommutative Hopf algebras.

Deformations of associative Rota-Baxter operators

Rota–Baxter operators on groups

The theory of Rota–Baxter operators on rings and algebras has been developed since 1960. In 2020, the notion of Rota–Baxter operator on a group was defined. Further, it was proved that one may define

An integral formula for cocycles of Lie groups

2014 The relationship between cohomology of Lie groups and of Lie algebras is studied, locally as well globally, by means of a formalism associating some differential forms with Cx cochains. An

The Weil algebra and the Van Est isomorphism

This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the

The $L_\infty$-deformations of associative Rota-Baxter algebras and homotopy Rota-Baxter operators

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

Differentiable and algebroid cohomology, Van Est isomorphisms, and characteristic classes

AbstractIn the first section we discuss Morita invariance of differentiable/algebroid cohomology.In the second section we extend the Van Est isomorphism to groupoids. As a first application we

Integrating central extensions of Lie algebras via Lie 2-groups

The purpose of this paper is to show how central extensions of (possibly infinite-dimensional) Lie algebras integrate to central extensions of \'etale Lie 2-groups. In finite dimensions, central