VECTOR-FIELDS AS DERIVATIONS ON NUCLEAR MANIFOLDS

If M is a manifold modelled over a nuclear Frechet space, the smooth v ector fields, as in the finite dimensional case, may be identified wit h continuous derivations in the space E(M) of real C-infinity function s on M. This applies for instance to the loop groups and the group of diffeomorphisms of the circle: M = E(S-1, G), M = Diff(S-1).