Higher multi-Courant algebroids

The binary bracket of a Courant algebroid structure on (E,〈⋅,⋅〉) can be extended to n-ary Γ(E), yielding multi-Courant algebroid. These brackets form Poisson algebra and were defined, in an algebraic setting, by Keller Waldmann. We construct higher geometric version Keller-Waldmann define algebroids. As structures seen as degree 3 functions graded symplectic manifold 2, n≥3 that manifold.