Geodesic
Alg�bres de Lie 2-Nilpotentes et Structures Symplectiques
Journal of Lie theory, Tome 23 (2013) no. 1, pp. 217-228.

Voir la notice de l'article provenant de la source Heldermann Verlag

2-step nilpotent Lie algebras are finite dimensional Lie algebras A over a field with [[x,y],z] = 0 for all x,y,z of A. Each of them is a direct product of an abelian ideal and an ideal B with DB = ZB and we get three numerical invariants r = dim I, s = dim DA = dim DB. To classify these algebras, it is enough to consider only the case r = 0 (or DA = ZA) and we call (t,s) the type of A. In the article "Alg�bre de Lie m�tab�liennes" [Ann. Facult� des Sciences Toulouse II (1980) 93--100] Ph. Revoy used the Scheuneman invariant [see J. Scheuneman, Two-step nilpotent Lie algebras, J. of Algebra 7 (1967) 152--159] to describe some of these; the aim of this paper is to complete and to make precise our earlier results, especially the case of s=2 or 3.
Classification : 17B30
Mots-clés : Two-step nilpotent Lie algebras, symplectic Lie algebras 
@article{JLT_2013_23_1_JLT_2013_23_1_a11,
     author = {N. Midoune },
     title = {Alg�bres de {Lie} {2-Nilpotentes} et {Structures} {Symplectiques}},
     journal = {Journal of Lie theory},
     pages = {217--228},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2013},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a11/}
}
TY  - JOUR
AU  - N. Midoune 
TI  - Alg�bres de Lie 2-Nilpotentes et Structures Symplectiques
JO  - Journal of Lie theory
PY  - 2013
SP  - 217
EP  - 228
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a11/
ID  - JLT_2013_23_1_JLT_2013_23_1_a11
ER  - 
%0 Journal Article
%A N. Midoune 
%T Alg�bres de Lie 2-Nilpotentes et Structures Symplectiques
%J Journal of Lie theory
%D 2013
%P 217-228
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a11/
%F JLT_2013_23_1_JLT_2013_23_1_a11
N. Midoune . Alg�bres de Lie 2-Nilpotentes et Structures Symplectiques. Journal of Lie theory, Tome 23 (2013) no. 1, pp. 217-228. http://geodesic.mathdoc.fr/item/JLT_2013_23_1_JLT_2013_23_1_a11/