290 citations · 1.2k across the 89 of their papers we have counts for
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Crossed homomorphisms and Cartier-Kostant-Milnor-Moore theorem for difference Hopf algebras
Li Guo, Yunnan Li, Yunhe Sheng +1
The celebrated Milnor-Moore theorem and the more general Cartier-Kostant-Milnor-Moore theorem establish close relationships of a connected and a pointed cocommutative Hopf algebra…
Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras
Honglei Lang, Yunhe Sheng
In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie…
Reynolds -Lie algebras and NS--Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we introduce the notion of a Reynolds operator on an -Lie algebra and illustrate the relationship between Reynolds operators and derivations on an -Lie a…
Representations and cohomologies of relative Rota-Baxter Lie algebras and applications
Jun Jiang, Yunhe Sheng
In this paper, first we give the notion of a representation of a relative Rota-Baxter Lie algebra and introduce the cohomologies of a relative Rota-Baxter Lie algebra with coeffici…
Relative Rota-Baxter operators and symplectic structures on Lie-Yamaguti algebras
Yunhe Sheng, Jia Zhao
In this paper, first we introduce the notion of a quadratic Lie-Yamaguti algebra and show that the invariant bilinear form in a quadratic Lie-Yamaguti algebra induces an isomorphis…
Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures
Meijun Liu, Jiefeng Liu, Yunhe Sheng
Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give t…
Lie theory and cohomology of relative Rota-Baxter operators
Jun Jiang, Yunhe Sheng, Chenchang Zhu
In this paper, we establish a local Lie theory for relative Rota-Baxter operators of weight . First we recall the category of relative Rota-Baxter operators of weight on Lie…
Twisted Rota-Baxter operators on 3-Lie algebras and NS-3-Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we introduce the notion of a twisted Rota-Baxter operator on a 3-Lie algebra $\g$ with a representation on . We show that a twisted Rota-Baxter operator ind…
Maurer-Cartan characterizations and cohomologies of compatible Lie algebras
Jifeng Liu, Yunhe Sheng, Chengming Bai
In this paper, we give Maurer-Cartan characterizations as well as a cohomology theory for compatible Lie algebras. Explicitly, we first introduce the notion of a bidifferential gra…