Geodesic
Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
Journal of Lie theory, Tome 24 (2014) no. 3, pp. 889-908.

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

We introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely, the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.
Classification : 17B30, 17B56, 55T05, 53D05
Mots-clés : Symplectic structures, nilpotent Lie algebras, Lie algebra cohomolgy, minimal parabolic subalgebras 
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     author = {V. Del Barco },
     title = {Symplectic {Structures} on {Nilmanifolds:} an {Obstruction} for their {Existence}},
     journal = {Journal of Lie theory},
     pages = {889--908},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a13/}
}
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V. Del Barco . Symplectic Structures on Nilmanifolds: an Obstruction for their Existence. Journal of Lie theory, Tome 24 (2014) no. 3, pp. 889-908. http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a13/