2020/04/06 by Augustin T. Batubenge, Batubenge, Augustin T., Wallace M. Haziyu +1
Mathematics · #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2004.02507
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.