Geodesic
Invariant Lie Algebras and Lie Algebras with a~Small Centroid
Algebra i logika, Tome 40 (2001) no. 6, pp. 651-674.

Voir la notice de l'article provenant de la source Math-Net.Ru

A subalgebra of a Lie algebra is said to be invariant if it is invariant under the action of some Cartan subalgebra of that algebra. A known theorem of Melville says that a nilpotent invariant subalgebra of a finite-dimensional semisimple complex Lie algebra has a small centroid. The notion of a Lie algebra with small centroid extends to a class of all finite-dimensional algebras. For finite-dimensional algebras of zero characteristic with semisimple derivations in a sufficiently broad class, their centroid is proved small. As a consequence, it turns out that every invariant subalgebra of a finite-dimensional reductive Lie algebra over an arbitrary definition field of zero characteristic has a small centroid.
Keywords: Lie algebra, finite-dimensional Lie algebra, reductive Lie algebra, nilpotent algebra
Mots-clés : invariant subalgebra, Cartan subalgebra, centroid. 
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     author = {K. N. Ponomarev},
     title = {Invariant {Lie} {Algebras} and {Lie} {Algebras} with {a~Small} {Centroid}},
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K. N. Ponomarev. Invariant Lie Algebras and Lie Algebras with a~Small Centroid. Algebra i logika, Tome 40 (2001) no. 6, pp. 651-674. http://geodesic.mathdoc.fr/item/AL_2001_40_6_a1/