  A 2-plectic manifold is a manifold equipped with a closed nondegenerate
3-form, just as a symplectic manifold is equipped with a closed nondegenerate
2-form. In 2-plectic geometry we meet higher analogues of many structures
familiar from symplectic geometry. For example, any 2-plectic manifold has a
Lie 2-algebra consisting of smooth functions and Hamiltonian 1-forms. This is
equipped with a Poisson-like bracket which only satisfies the Jacobi identity
up to `coherent chain homotopy'. Over any 2-plectic manifold is a vector bundle
equipped with extra structure called an exact Courant algebroid. This Courant
algebroid is the 2-plectic analogue of a transitive Lie algebroid over a
symplectic manifold. Its space of global sections also forms a Lie 2-algebra.
We show that this Lie 2-algebra contains an important sub-Lie 2-algebra which
is isomorphic to the Lie 2-algebra of Hamiltonian 1-forms. Furthermore, we
prove that it is quasi-isomorphic to a central extension of the (trivial) Lie
2-algebra of Hamiltonian vector fields, and therefore is the higher analogue of
the well-known Kostant-Souriau central extension in symplectic geometry. We
interpret all of these results within the context of a categorified
prequantization procedure for 2-plectic manifolds. In doing so, we describe how
U(1)-gerbes, equipped with a connection and curving, and Courant algebroids are
the 2-plectic analogues of principal U(1) bundles equipped with a connection
and their associated Atiyah Lie algebroids.
