Automorphisms of cotangent bundles of Lie groups
نویسنده
چکیده
Let G be a Lie group, G its Lie algebra, T G its cotangent bundle and D := tG the Lie algebra of T G. 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
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