Geodesic
Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
Journal of Lie theory, Tome 24 (2014) no. 3, pp. 889-908 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 
@article{JLT_2014_24_3_JLT_2014_24_3_a13,
     author = {V. Del Barco },
     title = {Symplectic {Structures} on {Nilmanifolds:} an {Obstruction} for their {Existence}},
     journal = {Journal of Lie theory},
     pages = {889--908},
     year = {2014},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a13/}
}
TY  - JOUR
AU  - V. Del Barco 
TI  - Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
JO  - Journal of Lie theory
PY  - 2014
SP  - 889
EP  - 908
VL  - 24
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a13/
ID  - JLT_2014_24_3_JLT_2014_24_3_a13
ER  - 
%0 Journal Article
%A V. Del Barco 
%T Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
%J Journal of Lie theory
%D 2014
%P 889-908
%V 24
%N 3
%U http://geodesic.mathdoc.fr/item/JLT_2014_24_3_JLT_2014_24_3_a13/
%F JLT_2014_24_3_JLT_2014_24_3_a13
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/