290 citations · 1.2k across the 89 of their papers we have counts for
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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…
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…
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…
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…
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…
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…
The controlling -algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
Yunhe Sheng, Rong Tang, Chenchang Zhu
In this paper, we first construct the controlling algebras of embedding tensors and Lie-Leibniz triples, which turn out to be a graded Lie algebra and an -algebra respect…
Categorification of VB-Lie algebroids and VB-Courant algebroids
Yunhe Sheng
In this paper, first we introduce the notion of a $\VB$-Lie -algebroid, which can be viewed as the categorification of a $\VB$-Lie algebroid. The tangent prolongation of a Lie $…
Kupershmidt-(dual-)Nijenhuis structures on a Lie algebra with a representation
Yuwang Hu, Jiefeng Liu, Yunhe Sheng
In this paper, first we study infinitesimal deformations of a Lie algebra with a representation and introduce the notion of a Nijenhuis pair, which gives a trivial deformation of a…
Linearization of the higher analogue of Courant algebroids
Honglei Lang, Yunhe Sheng
In this paper, we show that the spaces of sections of the -th differential operator bundle $\dev^n E$ and the -th skew-symmetric jet bundle $\jet_n E$ of a vector bundle …
Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation
Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a Leibniz bialgebra and show that matched pairs of Leibniz algebras, Manin triples of Leibniz algebras and Leibniz bialgebras are eq…
Left-symmetric bialgebroids and their corresponding Manin triples
Jiefeng Liu, Yunhe Sheng, Chengming Bai
In this paper, we introduce the notion of a left-symmetric bialgebroid as a geometric generalization of a left-symmetric bialgebra and construct a left-symmetric bialgebroid from a…
Bialgebras, the classical Yang-Baxter equation and Manin triples for 3-Lie algebras
Chengming Bai, Li Guo, Yunhe Sheng
This paper studies two types of 3-Lie bialgebras whose compatibility conditions between the multiplication and comultiplication are given by local cocycles and double constructions…
Nijenhuis operators on -Lie algebras
Jiefeng Liu, Yunhe Sheng, Yanqiu Zhou +1
In this paper, we study -order deformations of an -Lie algebra and introduce the notion of a Nijenhuis operator on an -Lie algebra, which could give rise to trivial de…
Hom-Big Brackets: Theory and Applications
Liqiang Cai, Yunhe Sheng
In this paper, we introduce the notion of hom-big brackets, which is a generalization of Kosmann-Schwarzbach's big brackets. We show that it gives rise to a graded hom-Lie algebra.…
On hom-Lie algebras
Yunhe Sheng, Zhen Xiong
In this paper, first we show that $(\g,[\cdot,\cdot],α)$ is a hom-Lie algebra if and only if $(Λ\g^*,α^*,d)$ is an -differential graded commutative algebra. Then, we rev…
Categorification of Pre-Lie Algebras and Solutions of 2-graded Classical Yang-Baxter Equations
Yunhe Sheng
In this paper, we introduce the notion of a pre-Lie 2-algebra, which is a categorification of a pre-Lie algebra. We prove that the category of pre-Lie 2-algebras and the category o…
Deformations of Lie 2-algebras
Zhangju Liu, Yunhe Sheng, Tao Zhang
In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra $\g$ corresponds to a…
A new approach to hom-Lie bialgebras
Yunhe Sheng, Chengming Bai
In this paper, we introduce a new definition of a hom-Lie bialgebra, which is equivalent to a Manin triple of hom-Lie algebras. We also introduce a notion of an -operat…
The Pontryagin Class for Pre-Courant Algebroids
Zhangju Liu, Yunhe Sheng, Xiaomeng Xu
In this paper, we show that the Jacobiator of a pre-Courant algebroid is closed naturally. The corresponding equivalence class is defined as the Pontryagin class, w…
Non-abelian Extensions of Lie 2-algebras
Shaohan Chen, Yunhe Sheng, Zhujun Zheng
In this paper, we introduce the notion of derivations of Lie 2-algebras and construct the associated derivation Lie 3-algebra. We prove that isomorphism classes of non-abelian exte…
Hom-Lie 2-algebras
Yunhe Sheng, Danhua Chen
In this paper, we introduce the notions of hom-Lie 2-algebras, which is the categorification of hom-Lie algebras, -algebras, which is the hom-analogue of -alge…
Integration of Lie 2-algebras and their morphisms
Yunhe Sheng, Chenchang Zhu
Given a strict Lie 2-algebra, we can integrate it to a strict Lie 2-group by integrating the corresponding Lie algebra crossed module. On the other hand, the integration procedure…