39 citations · 162 across the 33 of their papers we have counts for
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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…