Structure of the Coadjoint Orbits of Lie Algebras

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 give a new insight into the structure of coadjoint orbits and allow 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.