TY - JOUR
T1 - On regular Courant algebroids
AU - Chen, Zhuo
AU - Stiénon, Mathieu
AU - Xu, Ping
PY - 2013/3
Y1 - 2013/3
N2 - 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 H3DR(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 H3(g). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.
AB - 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 H3DR(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 H3(g). We also give a complete classification of regular Courant algebroids and discuss its relation to the characteristic class.
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U2 - 10.4310/JSG.2013.v11.n1.a1
DO - 10.4310/JSG.2013.v11.n1.a1
M3 - Article
AN - SCOPUS:84873321124
SN - 1527-5256
VL - 11
SP - 1
EP - 24
JO - Journal of Symplectic Geometry
JF - Journal of Symplectic Geometry
IS - 1
ER -