290 citations · 1.2k across the 89 of their papers we have counts for
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A new approach to representations of -Lie algebras and abelian extensions
Jiefeng Liu, Abdenacer Makhlouf, Yunhe Sheng
In this paper, we introduce the notion of generalized representation of a -Lie algebra, by which we obtain a generalized semidirect product -Lie algebra. Moreover, we develop…
Hom-Lie algebroids, Hom-Lie bialgebroids and Hom-Courant algebroids
Liqiang Cai, Jiefeng Liu, Yunhe Sheng
In this paper, first we modify the definition of a Hom-Lie algebroid introduced by Laurent-Gengoux and Teles and give its equivalent dual description. Many results that parallel to…
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…
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…
Pre-symplectic algebroids and their applications
Jiefeng Liu, Yunhe Sheng, Chengming Bai
In this paper, we introduce the notion of a pre-symplectic algebroid, and show that there is a one-to-one correspondence between pre-symplectic algebroids and symplectic Lie algebr…
QP-structures of degree 3 and CLWX 2-algebroids
Jiefeng Liu, Yunhe Sheng
In this paper, we give the notion of a CLWX 2-algebroid and show that a QP-structure of degree 3 gives rise to a CLWX 2-algebroid. This is the higher analogue of the result that a…
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…
On non-abelian extensions of Leibniz algebras
Jiefeng Liu, Yunhe Sheng, Qi Wang
In this paper, first we classify non-abelian extensions of Leibniz algebras by the second non-abelian cohomology. Then, we construct Leibniz 2-algebras using derivations of Leibniz…