On the rigidity of real solvable Lie algebras of rank one
The main objetive of this memoir is the study and classification of solvable rigid Lie algebras of rank one associated to certain types of eigenvalues spectra for a maximal torus of derivationson its nilradical. The employed techniques are the Chevalley cohomology of Lie algebras and the theory of d...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/105168 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/105168 |
| Access Level: | acceso abierto |
| Palabra clave: | 512(043.2) Álgebra 1201 Álgebra |
| Sumario: | The main objetive of this memoir is the study and classification of solvable rigid Lie algebras of rank one associated to certain types of eigenvalues spectra for a maximal torus of derivationson its nilradical. The employed techniques are the Chevalley cohomology of Lie algebras and the theory of deformations, as well as the Jacobi scheme. For the study of spectra in arbitrary dimensions, a specific code in the Mathematica® language has been developed. The principal results of this study are reunited in five research papers published in specialized journals. This structures the thesis into six chapters, that are structured as follows: In Chapter one the main structural results are recalled, mainly concerning the cohomological and geometrical analysis of rigidity. We also present a schematic description of the contents of these articles, as well as the symbolic computer package used for the computation of the cohomology groups with values in the adjoint module, illustrating it by an example. The chapter is closed with some conclusions as well as a description of potential prospective research lines, some of which are currently being analyzed. In Chapters 2-6, the five articles are reproduced (without the journal format). |
|---|