On higher dimensional exact Courant algebroids

Abstract

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 of O X ♯ [ n ] -extensions of T X ♯ .