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arXiv · 1210.6296

Symplectic structures on nilmanifolds: an obstruction for its existence

Viviana J. del Barco
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Abstract

In this work 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.

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Viviana J. del Barco. 2012-10-23. Symplectic structures on nilmanifolds: an obstruction for its existence. https://arxiv.org/abs/1210.6296

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