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.
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