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On higher-dimensional Courant algebroids. (English) Zbl 1397.53092

In this paper, the authors describe a construction which to any Courant algebroid associates a Lie algebroid. To this end, they introduce a transgression functor. After some recalls about the theory of differential graded manifolds and of the classification of Courant algebroids, the authors introduce their construction. The results are then proved. Finally, they prove that in the case of Courant extensions, transgression restricts to an equivalence of appropriately defined categories.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
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