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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/732| MATRIX LIE GROUPS AND LIE CORRESPONDENCES | |
| MONYRATTANAK SENG | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| MATRIX LIE GROUPS | |
| Lie group is a differentiable manifold equipped with a group structure in which the group multiplication and inversion are smooth. The tangent space at the identity of a Lie group is called Lie algebra. Most Lie groups are in (or isomorphic to) the matrix forms that is topologically closed in the complex general linear group. We call them matrix Lie groups. The Lie correspondences between Lie group and its Lie algebra allow us to study Lie group, which is an algebraic object in term of Lie algebra, which is a linear object. In this work, we concern about the two correspondences in the case of matrix Lie groups; namely, 1. The one-one correspondence between Lie group and it Lie algebra and 2. The one-one correspondence between Lie group homomorphism and Lie algebra homomorphism. However, the correspondences in the general case is not much different of those in the matrix case. To achieve these goals, we will present some matrix Lie groups and study their topological and algebraic properties. Then, we will construct their Lie algebras and develop some important properties that lead to the main result of the thesis. | |
| 02-08-2017 | |
| Trabajo de grado, maestría | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
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| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 639.pdf | 1.7 MB | Adobe PDF | Visualizar/Abrir |