1205.5898 (Zhangju Liu et al.)

Pre-Courant Algebroids and Associated Lie 2-Algebras    [PDF]

Zhangju Liu, Yunhe Sheng, Xiaomeng Xu

In this paper, we show that the Jacobiator of a pre-Courant algebroid has some remarkable properties. Thus we can construct both Leibniz 2-algebra and Lie 2-algebra structures associated to a pre-Courant algebroid and prove that these algebraic structures are stable under deformations. The Pontryagin class is also introduced for a pre-Courant algebroid as the obstruction to be deformed into a Courant algebroid. Finally, we introduce the twisted action of a Lie algebra on a manifold to give more examples of pre-Courant algebroids, which include the parabolic geometry.

View original: http://arxiv.org/abs/1205.5898