Abstract
For any regular Courant algebroid, we construct a characteristic class à 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 Ševera class in $H^3_{dR}(M)$. On the other hand, when the Courant algebroid is a quadratic Lie algebra $\mathfrak{g}$, it coincides with the class of the Cartan 3-form in $H^3(\mathfrak{g})$. We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.
Citation
Zhuo Chen. Mathieu Stiénon. Ping Xu. "On regular Courant algebroids." J. Symplectic Geom. 11 (1) 1 - 24, March 2013.
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