Journal of Symplectic Geometry

On regular Courant algebroids

Zhuo Chen, Mathieu Stiénon, and Ping Xu

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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.

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

First available in Project Euclid: 1 March 2013

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Chen, Zhuo; Stiénon, Mathieu; Xu, Ping. On regular Courant algebroids. J. Symplectic Geom. 11 (2013), no. 1, 1--24.

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