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 
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     title = {Alg�bres de {Lie} {2-Nilpotentes} et {Structures} {Symplectiques}},
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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/