On higher dimensional exact Courant algebroids

For a smooth manifold X we show an equivalence of categories between the category of O-X# [n]-extensions of T-X# and the category of higher-dimensional exact Courant algebroids on X. In addition, for any object in the category of R[n] dg-principal bundles over X-# we construct its Atiyah algebroid which gives rise to an example a O-X# [n]-extensions of T-X#. (C) 2016 Elsevier B.V. All rights reserved.