39 citations · 162 across the 33 of their papers we have counts for
33 papers
On the structure of finite Novikov conformal algebras
Pavel Kolesnikov, Jiefeng Liu
We classify finite simple Novikov conformal algebras over an algebraically closed field of characteristic zero. The classification consists of the current conformal algebra over th…
Affine Rota-Baxter groups and affine skew braces
Jiayao Ma, Boran Zhang, Jiefeng Liu
Rota-Baxter groups and skew braces are closely related algebraic structures, both providing set-theoretical solutions to the Yang-Baxter equation. In this paper, we extend these st…
Pre-vertex algebras, pre-Poisson vertex algebras and their deformation quantizations
Jiabao Xu, Jiefeng Liu
In this paper, we introduce pre-vertex algebras and pre-Poisson vertex algebras as preLie-algebras in the chiral and classical pseudo-tensor categories, respectively. We show that…
Hyper relative differential operators on Lie algebras
Sofiane Bouarroudj, Jiefeng Liu, Liwen Zhang
In this paper, we first introduce the notion of a hyper relative differential operator on a Lie algebra, in which Nijenhuis operators are used to characterize the relative differen…
From pre-Lie bialgebras to phase spaces of Lie algebras: a categorical correspondence
Qi Wang, Xueyi Wang, Jiefeng Liu
This paper establishes a categorical framework for phase spaces of Lie algebras, pre-Lie bialgebras, Manin triples, classical s-matrices, and relative Rota-Baxter operators by intr…
Twisting theory, relative Rota-Baxter type operators and -algebras on Lie conformal algebras
Lamei Yuan, Jiefeng Liu
Based on Nijenhuis-Richardson bracket and bidegree on the cohomology complex for a Lie conformal algebra, we develop a twisting theory of Lie conformal algebras. By using derived b…
Cohomology and deformation quantization of Poisson conformal algebras
Jiefeng Liu, Hongyu Zhou
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutat…
Conformal -matrix-Nijenhuis structures, symplectic-Nijenhuis structures and -structures
Jiefeng Liu, Sihan Zhou, Lamei Yuan
In this paper, we first study infinitesimal deformations of a Lie conformal algebra and a Lie conformal algebra with a module (called an pair), which lead to the n…
Rota-Baxter Lie -algebras
Shilong Zhang, Jiefeng Liu
In this paper, we introduce the notion of Rota-Baxter Lie -algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie -a…
Cohomologies and deformations of pre-Lie-morphism triples
Yibo Wang, Shilong Zhang, Jiefeng Liu
A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a (pre-)Lie algebra homomorphism between them. We give chomologies of pre-Lie-morphism triples. As an application…
Cohomologies and crossed modules for pre-Lie Rinehart algebras
Liangyun Chen, Meijun Liu, Jiefeng Liu
A pre-Lie-Rinehart algebra is an algebraic generalization of the notion of a left-symmetric algebroid. We construct pre-Lie-Rinehart algebras from r-matrices through Lie algebra ac…
Cohomologies of 3-Lie algebras with derivations
Senrong Xu, Jiefeng Liu
In this paper, we consider a 3-Lie algebra with a derivation (called a 3-LieDer pair). We define cohomology for a 3-LieDer pair with coefficients in a representation. We use this c…
Admissible Poisson bialgebras
Jinting Liang, Jiefeng Liu, Chengming Bai
An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives an equivalent presentation with only one operation for a Poisson algebra. We establish a bialgebra theory f…
Lie n-algebras and cohomologies of relative Rota-Baxter operators on n-Lie algebras
Ming Chen, Jiefeng Liu, Yao Ma
Based on the differential graded Lie algebra controlling deformations of an -Lie algebra with a representation (called an n-LieRep pair), we construct a Lie n-algebra, whose Mau…
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…
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…
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…
Noncommutative Poisson bialgebras
Jiefeng Liu, Chengming Bai, Yunhe Sheng
In this paper, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebr…
Pre-Lie analogues of Poisson-Nijenhuis structures and Maurer-Cartan equations
Jiefeng Liu, Qi Wang
In this paper, we study pre-Lie analogues of Poisson-Nijenhuis structures and introduce ON-structures on bimodules over pre-Lie algebras. We show that an ON-structure gives rise to…
Twisting on pre-Lie algebras and quasi-pre-Lie bialgebras
Jiefeng Liu
We study (quasi-)twilled pre-Lie algebras and the associated -algebras and differential graded Lie algebras. Then we show that certain twisting transformations on (quasi-…
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…
Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
Jiefeng Liu, Yunhe Sheng
In this paper, we construct a homotopy Poisson algebra of degree 3 associated to a split Lie 2-algebroid, by which we give a new approach to characterize a split Lie 2-bialgebroid.…
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…