On Regular Courant Algebroids
Differential Geometry
2021-06-07 v3 Mathematical Physics
math.MP
Abstract
For any regular Courant algebroid, we construct a characteristic class a la Chern-Weil. This intrinsic invariant of the Courant algebroid is a degree-3 class in its naive cohomology. When the Courant algebroid is exact, it reduces to the Severa class (in H^3_{DR}(M)). On the other hand, when the Courant algebroid is a quadratic Lie algebra g, it coincides with the class of the Cartan 3-form (in H^3(g)). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.
Cite
@article{arxiv.0909.0319,
title = {On Regular Courant Algebroids},
author = {Zhuo Chen and Mathieu Stienon and Ping Xu},
journal= {arXiv preprint arXiv:0909.0319},
year = {2021}
}
Comments
Section 3.3 and references added; An error about classification is corrected