290 citations · 1.2k across the 89 of their papers we have counts for
21 papers · 1 filter
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.…
Affine structures on Lie groupoids
Honglei Lang, Zhangju Liu, Yunhe Sheng
Affine structures on a Lie groupoid, including affine -vector fields, -forms and -tensors are studied. We show that the space of affine structures is a 2-vector space…
Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation
Jun Jiang, Satyendra Kumar Mishra, Yunhe Sheng
In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Th…
The first Pontryagin class of a quadratic Lie 2-algebroid
Yunhe Sheng
In this paper, first we give a detailed study on the structure of a transitive Lie 2-algebroid and describe a transitive Lie 2-algebroid using a morphism from the tangent Lie algeb…
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…
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…
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…
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…
Integration of derivations for Lie -algebras
Honglei Lang, Zhangju Liu, Yunhe Sheng
In this paper, for a Lie 2-algebra $\g$, we construct the automorphism 2-group $\Aut(\g)$, which turns out to be an integration of the derivation Lie 2-algebra $\Der(\g)$.
Left-symmetric algebroids
Jiefeng Liu, Yunhe Sheng, Chengming Bai +1
In this paper, we introduce a notion of a left-symmetric algebroid, which is a generalization of a left-symmetric algebra from a vector space to a vector bundle. The left multiplic…
Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
Honglei Lang, Yunhe Sheng, Xiaomeng Xu
We study Maurer-Cartan elements on homotopy Poisson manifolds of degree . They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as tw…
On Double Vector Bundles
Zhuo Chen, Zhangju Liu, Yunhe Sheng
In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on…
On deformations of Lie algebroids
Yunhe Sheng
For any Lie algebroid A, its 1-jet bundle JA is a Lie algebroid naturally and there is a representation π: JA ->DA. Denote by dJ the corresponding coboundary operator. In this pape…
On higher analogues of Courant algebroids
Yanhui Bi, Yunhe Sheng
In this paper, we study the algebraic properties of the higher analogues of Courant algebroid structures on the direct sum bundle for an -dimensional mani…
Integration of semidirect product Lie 2-algebras
Yunhe Sheng, Chenchang Zhu
The semidirect product of a Lie algebra and a 2-term representation up to homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising from the Courant algebroid…
Semidirect products of representations up to homotopy
Yunhe Sheng, Chenchang Zhu
We study the semidirect product of a Lie algebra with a representation up to homotopy and provide various examples coming from Courant algebroids, string Lie 2-algebras, and omni-L…
E-Courant algebroids
Zhuo Chen, Zhangju Liu, Yunhe Sheng
In this paper, we introduce the notion of -Courant algebroids, where is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Coura…
Dirac structures of omni-Lie algebroids
Zhuo Chen, Zhangju Liu, Yunhe Sheng
Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid $\dev E\oplus \jet E$ is necessarily a Lie algebroid toget…
Linear Poisson structures on R^4
Yunhe Sheng
We classify all of the 4-dimensional linear Poisson structures of which the corresponding Lie algebras can be considered as the extension by a derivation of 3-dimensional unimodula…
Quadratic Deformations of Lie-Poisson Structures
Qian Lin, Zhangju Liu, Yunhe Sheng
In this letter, first we give a decomposition for any Lie-Poisson structure associated to the modular vector. In particular, splits into two compatible Lie-Poisson stru…