Journal of Lie Theory

no. 1
Structure of the Coadjoint Orbits of Lie Algebras
Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 251-268
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.
DOI: 10.5802/jolt.668
Classification: 57S25, 17B45, 22E45, 53D20
Keywords: Coadjoint orbit, integral coadjoint orbit 
@article{JOLT_2012_22_1_a9,
     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},
     doi = {10.5802/jolt.668},
     zbl = {1323.17010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.668/}
}
TY  - JOUR
AU  - I. V. Mykytyuk
TI  - Structure of the Coadjoint Orbits of Lie Algebras
JO  - Journal of Lie Theory
PY  - 2012
SP  - 251
EP  - 268
VL  - 22
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.668/
DO  - 10.5802/jolt.668
ID  - JOLT_2012_22_1_a9
ER  - 
%0 Journal Article
%A I. V. Mykytyuk
%T Structure of the Coadjoint Orbits of Lie Algebras
%J Journal of Lie Theory
%D 2012
%P 251-268
%V 22
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.668/
%R 10.5802/jolt.668
%F JOLT_2012_22_1_a9
I. V. Mykytyuk. Structure of the Coadjoint Orbits of Lie Algebras. Journal of Lie Theory, Volume 22 (2012) no. 1, pp. 251-268. doi: 10.5802/jolt.668

Cited by Sources: