The Nash–Moser theorem of Hamilton and rigidity of finite dimensional nilpotent Lie algebras
We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the spac...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/59986 |
| Acceso en línea: | http://hdl.handle.net/11336/59986 |
| Access Level: | acceso abierto |
| Palabra clave: | deformations and rigidity Lie algebras Cohomology of Lie algebras https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We apply the Nash–Moser theorem for exact sequences of R. Hamilton to the context of deformations of Lie algebras and we discuss some aspects of the scope of this theorem in connection with the polynomial ideal associated to the variety of nilpotent Lie algebras. This allows us to introduce the space Hk-nil 2(g,g), and certain subspaces of it, that provide fine information about the deformations of g in the variety of k-step nilpotent Lie algebras. Then we focus on degenerations and rigidity in the variety of k-step nilpotent Lie algebras of dimension n with n≤7 and, in particular, we obtain rigid Lie algebras and rigid curves in the variety of 3-step nilpotent Lie algebras of dimension 7. We also recover some known results and point out a possible error in a published article related to this subject. |
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