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arXiv · 2004.02507

On the case where Adjoint and Coadjoint Orbit Spaces are Symplectomorphic

Augustin T. Batubenge·Wallace M. Haziyu
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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.

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Augustin T. Batubenge, Wallace M. Haziyu. 2020-04-06. On the case where Adjoint and Coadjoint Orbit Spaces are Symplectomorphic. https://arxiv.org/abs/2004.02507

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