39 citations · 162 across the 33 of their papers we have counts for
7 papers · 1 filter
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.…