Geodesic
Solvable Lie algebras and maximal Abelian dimensions
Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1 
Á. F. Tenorio. Solvable Lie algebras and maximal Abelian dimensions. Acta mathematica Universitatis Comenianae, Tome 77 (2008) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a11/
@article{AMUC_2008_77_1_a11,
     author = {\'A. F. Tenorio},
     title = {Solvable {Lie} algebras and maximal {Abelian} dimensions},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2008},
     volume = {77},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2008_77_1_a11/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal abelian dimension is applied to characterize the n -dimensional nilpotent Lie algebras with maximal abelian dimension equal to their codimension.