Automorphisms of Cotangent Bundles of Lie Groups

Let G be a Lie group, G its Lie algebra, TG its cotangent bundle and D := tG the Lie algebra of TG. We investigate the group of automorphisms of D. More precisely, we fully characterize the space of all derivations of D. As a byproduct, we also characterize some spaces of operators on G amongst which the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or pseudo-Riemannian metric, then J is isomorphic to the space of equivariant linear maps G � → G, as well as that of bi-invariant bilinear forms on G. 1