摘要
首先分别从范畴化和L-无穷代数两个不同角度回顾了李2-代数的两种等价定义.接着给出了从4种几何结构中产生的李2-代数.进一步,阐述了李2-代数的上同调理论并具体分析了低阶情况.最后讨论了严格李2-代数到严格李2-群的积分.
We first recall two equivalent definitions of Lie 2-algebras,categorification of Lie algebras and 2-term L_∞-algebras.Then we present four different kinds of Lie 2-algebras from 2-plectic manifolds,Courant algebroids,homotopy Poisson manifolds and affine multivector fields on a Lie groupoid respectively.Moreover,we recall the cohomology theory of Lie 2-algebras and analyze its lower degree cases.The integration of strict Lie 2-algebras to strict Lie 2-groups is also discussed.
作者
郎红蕾
刘张炬
LANG Honglei;LIU Zhangju(Department of Applied Mathematics,China Agricultural University,Beijing,100083,P.R.China;School of Mathematical Sciences,Peking University,Beijing,100871,P.R.China)
出处
《数学进展》
CSCD
北大核心
2020年第6期641-674,共34页
Advances in Mathematics（China）
基金
Supported by NSFC(Nos.11901568,12071241)。
关键词
李2-代数
范畴化
上同调
李2-群
Lie 2-algebras
categorification
cohomology
Lie 2-groups
作者简介
LANG Honglei,E-mail:hllang@cau.edu.cn;Corresponding author:LIU Zhangju,liuzj@pku.edu.cn。
