Automorphisms of cotangent bundles of Lie groups
  Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action of G on the dual space of its Lie algebra.   We investigate the group of automorphisms of the Lie algebra of $T^*G$. More precisely, amongst other results, we fully characterize the space of all derivations of the Lie algebra of $T^*G$.   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 linear maps from the Lie algebra of G to its dual space which are equivariant with respect to the adjoint and coadjoint actions, as well as that of bi-invariant bilinear forms on G.   We discuss some open problems and possible applications. 
Andre Diatta and Bakary Manga