## Journal of Symplectic Geometry

### On regular Courant algebroids

#### 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.

#### Article information

Source
J. Symplectic Geom., Volume 11, Number 1 (2013), 1-24.

Dates
First available in Project Euclid: 1 March 2013