Left invariant special Kähler structures
We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double...
- Autores:
-
Valencia Quintero, Fabricio
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2022
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/46171
- Acceso en línea:
- https://hdl.handle.net/10495/46171
- Palabra clave:
- Álgebras de Lie
Lie algebras
Álgebras lineales
Algebras, linear
Estructuras especiales de Kähler
Propiedad Hessiana
Twisted cartesian products
Special Kähler structures
Hessian property
Productos cartesianos torcidos
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| Summary: | We construct left invariant special Kähler structures on the cotangent bundle of a flat pseudo-Riemannian Lie group. We introduce the twisted cartesian product of two special Kähler Lie algebras according to two linear representations by infinitesimal Kähler transformations. We also exhibit a double extension process of a special Kähler Lie algebra which allows us to get all simply connected special Kähler Lie groups with bi-invariant symplectic connections. All Lie groups constructed by performing this double extension process can be identified with a subgroup of symplectic (or Kähler) affine transformations of its Lie algebra containing a nontrivial 1-parameter subgroup formed by central translations. We show a characterization of left invariant flat special Kähler structures using étale Kähler affine representations, exhibit some immediate consequences of the constructions mentioned above, and give several non-trivial examples. |
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