English

On the case where Adjoint and Coadjoint Orbit Spaces are Symplectomorphic

Symplectic Geometry 2020-04-07 v1

Abstract

Let G be an n-dimensional semisimple compact and connected Lie group acting on both the Lie algebra g of G and its dual g*. We show that a nondegenerate Killing form of G induces an Ad*-equivariant isomorphism of g onto g* which, in turn, induces by passage to quotients a symplectomorphism between adjoint and coadjoint orbit spaces of G.

Keywords

Cite

@article{arxiv.2004.02507,
  title  = {On the case where Adjoint and Coadjoint Orbit Spaces are Symplectomorphic},
  author = {Augustin T. Batubenge and Wallace M. Haziyu},
  journal= {arXiv preprint arXiv:2004.02507},
  year   = {2020}
}