Symplectic structures on nilmanifolds: an obstruction for its existence
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...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2014 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/30806 |
| Acceso en línea: | http://hdl.handle.net/11336/30806 |
| Access Level: | acceso abierto |
| Palabra clave: | Symplectic Structures Nilpotent Lie Algebras Lie Algebra Cohomology Minimal Parabolic Subalgebras https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | 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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