  Arnold showed that the Euler equations of an ideal fluid describe geodesics
in the Lie algebra of incompressible vector fields. We will show that helicity
induces a splitting of the Lie algebra into two isotropic subspaces, forming a
Manin triple. Viewed another way, this shows that there is an infinitesimal
quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.
