H. Lang

activity

20182021

collaborators

5 papers

math.RA2021

A review of Lie 2-algebras

Honglei Lang, Zhangju Liu

We first recall two equivalent definitions of Lie $2$ -algebras, categorification of Lie algebras and $2$ -term $L_{\infty}$ -algebras. Then we present four different kinds of Lie $2$ -a…

math-ph2020

Linearization of the higher analogue of Courant algebroids

Honglei Lang, Yunhe Sheng

In this paper, we show that the spaces of sections of the $n$ -th differential operator bundle $\dev^n E$ and the $n$ -th skew-symmetric jet bundle $\jet_n E$ of a vector bundle $E$ …

math.QA2019

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…

math.DG2019

Affine structures on Lie groupoids

Honglei Lang, Zhangju Liu, Yunhe Sheng

Affine structures on a Lie groupoid, including affine $k$ -vector fields, $k$ -forms and $(p, q)$ -tensors are studied. We show that the space of affine structures is a 2-vector space…

math.DG2018

Coadjoint orbits of Lie groupoids

Honglei Lang, Zhangju Liu

For a Lie groupoid $G$ with Lie algebroid $A$ , we realize the symplectic leaves of the Lie-Poisson structure on $A^{*}$ as orbits of the affine coadjoint action of the Lie…