Leibniz 2-algebras and twisted Courant algebroids

Sheng Yunhe; Liu Zhangju

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Leibniz 2-algebras and twisted Courant algebroids

Sheng Yunhe 1,Liu Zhangju 2 *

1.Department of Mathematics, Jilin University, ChangChun 130012

2.Department of Mathematics, Peking University, Beijing 100871

*Correspondence author

#Submitted by

Subject:

Funding: Doctoral Fund. of MEC （No.20100061120096）, NSF of China（No.11026046,11101179）

Opened online:21 March 2012

Accepted by: none

Citation: Sheng Yunhe ,Liu Zhangju .Leibniz 2-algebras and twisted Courant algebroids[OL]. [21 March 2012] http://en.paper.edu.cn/en_releasepaper/content/4468380

In this paper, the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras is given.They reveal the algebraic structure of omni-Lie 2-algebras as well as twisted Courant algebroidsby closed 4-forms. Dirac structures of twisted Courant algebroids give rise to 2-term L∞-algebras and geometric structures behind them areexactly H-twisted Lie algebroids

Keywords:Leibniz 2-algebra; omni-Lie2-algebras; twisted Courant algebroid; the first Pontryagin class; Dirac structure

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