Journal of Lie Theory

no. 3
Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 889-908
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.
DOI: 10.5802/jolt.811
Classification: 17B30, 17B56, 55T05, 53D05
Keywords: Symplectic structures, nilpotent Lie algebras, Lie algebra cohomolgy, minimal parabolic subalgebras 
@article{JOLT_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},
     doi = {10.5802/jolt.811},
     zbl = {1320.53098},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.811/}
}
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%A V. Del Barco
%T Symplectic Structures on Nilmanifolds: an Obstruction for their Existence
%J Journal of Lie Theory
%D 2014
%P 889-908
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%N 3
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%F JOLT_2014_24_3_a13
V. Del Barco. Symplectic Structures on Nilmanifolds: an Obstruction for their Existence. Journal of Lie Theory, Volume 24 (2014) no. 3, pp. 889-908. doi: 10.5802/jolt.811

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