 Both this standard example and the double of a Lie bialgebra are special instances of Courant algebroids.A Courant algebroid consists of the data a vector bundle formula_2 with a bracket formula_3, a non degenerate fiber-wise inner product formula_4, and a bundle map formula_5 subject to the following axioms,

where "φ,ψ,χ" are sections of "E" and "f" is a smooth function on the base manifold "M".