Geodesic
Structure of the Coadjoint Orbits of Lie Algebras
Journal of Lie theory, Tome 22 (2012) no. 1, pp. 251-268
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We study the geometrical structure of the coadjoint orbits of an arbitrary complex or real Lie algebra g containing some ideal n. It is shown that any coadjoint orbit in g* is a bundle with the affine subspace of g* as its fibre. This fibre is an isotropic submanifold of the orbit and is defined only by the coadjoint representations of the Lie algebras g and n on the dual space n*. The use of this fact gives a new insight into the structure of coadjoint orbits and allows us to generalize results derived earlier in the case when g is a semidirect product with an Abelian ideal n. As an application, a necessary condition of integrality of a coadjoint orbit is obtained.
Classification : 57S25, 17B45, 22E45, 53D20
Mots-clés : Coadjoint orbit, integral coadjoint orbit 
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     author = {I. V. Mykytyuk},
     title = {Structure of the {Coadjoint} {Orbits} of {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {251--268},
     year = {2012},
     volume = {22},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_1_JLT_2012_22_1_a9/}
}
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I. V. Mykytyuk. Structure of the Coadjoint Orbits of Lie Algebras. Journal of Lie theory, Tome 22 (2012) no. 1, pp. 251-268. http://geodesic.mathdoc.fr/item/JLT_2012_22_1_JLT_2012_22_1_a9/