290 citations · 1.2k across the 89 of their papers we have counts for
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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…
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…
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, 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…
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…
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…
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…
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…
Deformations of relative Rota-Baxter operators on Leibniz algebras
Rong Tang, Yunhe Sheng, Yanqiu Zhou
In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations o…
Cohomologies, extensions and deformations of differential algebras with any weights
Li Guo, Yunnan Li, Yunhe Sheng +1
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has…
Koszul-Vinberg structures and compatible structures on left-symmetric algebroids
Qi Wang, Jiefeng Liu, Yunhe Sheng
In this paper, we introduce the notion of Koszul-Vinberg-Nijenhuis structures on a left-symmetric algebroid as analogues of Poisson-Nijenhuis structures on a Lie algebroid, and sho…
F-manifold algebras and deformation quantization via pre-Lie algebras
Jiefeng Liu, Yunhe Sheng, Chengming Bai
The notion of an F-manifold algebra is the underlying algebraic structure of an -manifold. We introduce the notion of pre-Lie formal deformations of commutative associative alge…
Review of deformation theory I: Concrete formulas for deformations of algebraic structures
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie…
Symplectic, product and complex structures on 3-Lie algebras
Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre-Lie al…
Nijenhuis operators on pre-Lie algebras
Qi Wang, Chengming Bai, Jiefeng Liu +1
First we use a new approach to give a graded Lie algebra whose Maurer-Cartan elements characterize pre-Lie algebra structures. Then using this graded Lie bracket we define the noti…
Omni -Lie algebras and linearization of higher analogues of Courant algebroids
Jiefeng Liu, Yunhe Sheng, Chunyue Wang
In this paper, we introduce the notion of an omni -Lie algebra and show that they are linearization of higher analogues of standard Courant algebroids. We also introduce the not…
Purely Hom-Lie bialgebras
Liqiang Cai, Yunhe Sheng
In this paper, first we show that there is a Hom-Lie algebra structure on the set of -derivations of a commutative algebra. Then we construct dual representations of a repre…