72 citations · 120 across the 20 of their papers we have counts for
21 papers
Reflections on Rota-Baxter Lie algebras, the classical reflection equation and Poisson homogeneous spaces
Honglei Lang, Yunhe Sheng
In this paper, first we introduce the notion of reflections on quadratic Rota-Baxter Lie algebras of weight , and show that they give rise to solutions of the classical reflecti…
Poisson homogeneous spaces of Poisson 2-groups
Honglei Lang, Zhangju Liu
Drinfeld classified Poisson homogeneous spaces of a Poisson Lie group in terms of Dirac structures of the Lie bialgebra. In this paper, we study homogeneous spaces of a 2-group and…
The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid
Zhuo Chen, Honglei Lang, Zhangju Liu
Berwick-Evens and Lerman recently showed that the category of vector fields on a geometric stack has the structure of a Lie -algebra. Motivated by this work, we present a constr…
Dirac generating operators of split Courant algebroids
Liqiang Cai, Zhuo Chen, Honglei Lang +1
Given a vector bundle over a smooth manifold such that the square root of the line bundle …
Multiplicative forms on Poisson groupoids
Zhuo Chen, Honglei Lang, Zhangju Liu
Given a Lie groupoid over , the tangent Lie algebroid of , and the anchor map, we provide a formula that decomposes an arbitr…
Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras
Honglei Lang, Yunhe Sheng
In this paper, first we introduce the notion of quadratic Rota-Baxter Lie algebras of arbitrary weight, and show that there is a one-to-one correspondence between factorizable Lie…
A review of Lie 2-algebras
Honglei Lang, Zhangju Liu
We first recall two equivalent definitions of Lie -algebras, categorification of Lie algebras and -term -algebras. Then we present four different kinds of Lie -a…
The Atiyah class of generalized holomorphic vector bundles
Honglei Lang, Xiao Jia, Zhangju Liu
We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bu…
Integration and geometrization of Rota-Baxter Lie algebras
Li Guo, Honglei Lang, Yunhe Sheng
This paper first introduces the notion of a Rota-Baxter operator (of weight ) on a Lie group so that its differentiation gives a Rota-Baxter operator on the corresponding Lie al…
On the reduced space of multiplicative multivectors
Zhuo Chen, Honglei Lang, Zhangju Liu
A strict Lie -algebra is associated with any Lie groupoid . Here,…
Linearization of the higher analogue of Courant algebroids
Honglei Lang, Yunhe Sheng
In this paper, we show that the spaces of sections of the -th differential operator bundle $\dev^n E$ and the -th skew-symmetric jet bundle $\jet_n E$ of a vector bundle …
On Lie Bialgebroid Crossed Modules
Honglei Lang, Yu Qiao, Yanbin Yin
We study Lie bialgebroid crossed modules which are pairs of Lie algebroid crossed modules in duality that canonically give rise to Lie bialgebroids. A one-one correspondence betwee…
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…
Coadjoint orbits of Lie groupoids
Honglei Lang, Zhangju Liu
For a Lie groupoid with Lie algebroid , we realize the symplectic leaves of the Lie-Poisson structure on as orbits of the affine coadjoint action of the Lie…
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…
Double Principal Bundles
Honglei Lang, Yanpeng Li, Zhangju Liu
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown tha…
Atiyah classes of strongly homotopy Lie pairs
Zhuo Chen, Honglei Lang, Maosong Xiang
The subject of this paper is strongly homotopy (SH) Lie algebras, also known as -algebras. We extract an intrinsic character, the Atiyah class, which measures the nontriv…
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 $\Der(\g)$.
Crossed modules for Lie 2-algebras
Honglei Lang, Zhangju Liu
The notion of crossed modules for Lie 2-algebras is introduced. We show that, associated to such a crossed module, there is a strict Lie 3-algebra structure on its mapping cone com…
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…
Dirac and Generalized Complex Structures on Cartan Geometries
Honglei Lang, Xiaomeng Xu
We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on…