290 citations · 1.2k across the 89 of their papers we have counts for
90 papers
From Lie--Rinehart Algebras to -Manifold Algebras
Yufeng Pei, Yunhe Sheng
For every Lie--Rinehart algebra, we construct an -manifold algebra on the direct sum of its base algebra and module. Contrary to the assertion in \cite[Proposition 13.3.26]{Loda…
From relative Rota-Baxter operators and relative averaging operators on Lie algebras to relative Rota-Baxter operators on Leibniz algebras: a uniform approach
Rong Tang, Yunhe Sheng, Friedrich Wagemann
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz…
Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
Chengming Bai, Li Guo, Yunhe Sheng +1
The notions of a post-group and a pre-group are introduced as a unification and enrichment of several group structures appearing in diverse areas from numerical integration to the…
Omni-representations of Leibniz algebras
Zhangju Liu, Yunhe Sheng
In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space as a Leibniz algebra homomorphism from $\g$ to the omni-Lie a…
A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras
Yunhe Sheng
In this paper, we review deformation, cohomology and homotopy theories of relative Rota-Baxter Lie algebras, which have attracted quite much interest recently. Using Voronov's high…
Cohomologies of difference Lie groups and van Est theorem
Jun Jiang, Yunnan Li, Yunhe Sheng
A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce…
Deformations and homotopy of Rota-Baxter operators and -operators on Lie algebras
Rong Tang, Chengming Bai, Li Guo +1
This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally -operators on Lie algebras…
Deformations, cohomologies and abelian extensions of compatible -Lie algebras
Shuai Hou, Yunhe Sheng
In this paper, first we give the notion of a compatible -Lie algebra and construct a bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible -Lie algebr…
Deformations of modified -matrices and cohomologies of related algebraic structures
Jun Jiang, Yunhe Sheng
Modified -matrices are solutions of the modified classical Yang-Baxter equation, introduced by Semenov-Tian-Shansky, and play important roles in mathematical physics. In this pa…
Coherent categorical structures for Lie bialgebras, Manin triples, classical -matrices and pre-Lie algebras
Chengming Bai, Li Guo, Yunhe Sheng
The broadly applied notions of Lie bialgebras, Manin triples, classical -matrices and -operators of Lie algebras owe their importance to the close relationship amon…
Nonabelian embedding tensors
Rong Tang, Yunhe Sheng
In this paper, first we introduce the notion of a nonabelian embedding tensor, which is a nonabelian generalization of an embedding tensor. Then we introduce the notion of a Leibni…
-post-Lie algebras and relative Rota-Baxter operators of nonzero weight on -Lie algebras
Shuai Hou, Yunhe Sheng, Yanqiu Zhou
In this paper, first we introduce the notions of relative Rota-Baxter operators of nonzero weight on -Lie algebras and -post-Lie algebras. A 3-post-Lie algebra consists of a…
Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation
Yunnan Li, Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf al…
Deformations, cohomologies and integrations of relative difference Lie algebras
Jun Jiang, Yunhe Sheng
In this paper, first using the higher derived brackets, we give the controlling algebra of relative difference Lie algebras, which are also called crossed homomorphisms or differen…
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…
Twilled 3-Lie algebras, generalized matched pairs of 3-Lie algebras and O-operators
Shuai Hou, Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a twilled 3-Lie algebra, and construct an -algebra, whose Maurer-Cartan elements give rise to new twilled 3-Lie algebras b…