Automorphisms of cotangent bundles of Lie groups

Details Automorphisms of cotangent bundles of Lie groups Automorphisms of cotangent bundles of Lie groups

2008-11-18

arxiv.org/abs/0811.2951v1

Mathematics

Differential Geometry

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Automorphisms of cotangent bundles of Lie groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Automorphisms of cotangent bundles of Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Automorphisms of cotangent bundles of Lie groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101510