English

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.

Keywords

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

R2 v1 2026-06-21T13:41:27.113Z