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}
}