On Regular Courant Algebroids
Zhuo Chen, Mathieu Stienon, Ping Xu

TL;DR
This paper introduces a new characteristic class for regular Courant algebroids, generalizing known invariants like the Severa class and the Cartan 3-form, and provides a classification of these structures.
Contribution
It constructs an intrinsic degree-3 characteristic class for regular Courant algebroids and offers a complete classification linking this invariant to existing known classes.
Findings
The characteristic class reduces to the Severa class for exact Courant algebroids.
It coincides with the Cartan 3-form class for quadratic Lie algebras.
A full classification of regular Courant algebroids is provided.
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.
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