Published online by Cambridge University Press: 17 April 2009
We prove that the Lie algebra of infinitesimal automorphisms of the cotangent structure on the total space of the cotangent bundle of a manifold is isomorphic to the semi-direct product of the Lie algebra of the vector fields on the manifold by the space of closed 1-forms, the vector fields operating on the forms by Lie derivation. The derivations of this algebra Lie are completely determined and we prove that it characterises the cotangent bundle.