Extending invariant complex structures
We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h subset of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metri...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/24248 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/24248 |
| Access Level: | acceso abierto |
| Palabra clave: | 514.7 Complex structure Extension problem (extended) Semi-direct products Hermitian and anti-Hermitian structures Lie algebras with complex structures Geometría diferencial 1204.04 Geometría Diferencial |
| Sumario: | We study the problem of extending a complex structure to a given Lie algebra g, which is firstly defined on an ideal h subset of g. We consider the next situations: h is either complex or it is totally real. The next question is to equip g with an additional structure, such as a (non)-definite metric or a symplectic structure and to ask either h is non-degenerate, isotropic, etc. with respect to this structure, by imposing a compatibility assumption. We show that this implies certain constraints on the algebraic structure of g. Constructive examples illustrating this situation are shown, in particular computations in dimension six are given |
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