290 citations · 1.2k across the 89 of their papers we have counts for
7 papers · 1 filter
Symplectic, product and complex structures on 3-Lie algebras
Yunhe Sheng, Rong Tang
In this paper, first we introduce the notion of a phase space of a 3-Lie algebra and show that a 3-Lie algebra has a phase space if and only if it is sub-adjacent to a 3-pre-Lie al…
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…
Cohomological characterizations of non-abelian extensions of strict Lie 2-algebras
Rong Tang, Yunhe Sheng
In this paper, we study non-abelian extensions of strict Lie 2-algebras via the cohomology theory. A non-abelian extension of a strict Lie 2-algebra $\g$ by $\frkh$ gives rise to a…
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…
VB-Courant algebroids, E-Courant algebroids and generalized geometry
Honglei Lang, Yunhe Sheng, Aissa Wade
In this paper, we first discuss the relation between VB-Courant algebroids and E-Courant algebroids and construct some examples of E-Courant algebroids. Then we introduce the notio…
Omni -Lie algebras and linearization of higher analogues of Courant algebroids
Jiefeng Liu, Yunhe Sheng, Chunyue Wang
In this paper, we introduce the notion of an omni -Lie algebra and show that they are linearization of higher analogues of standard Courant algebroids. We also introduce the not…
String principal bundles and Courant algebroids
Yunhe Sheng, Xiaomeng Xu, Chenchang Zhu
Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of -gerb…