As esferas que admitem uma estrutura de grupo de Lie

We will show that the only connected Euclidean spheres admitting a structure of Lie group are S1 and S3, for all n greater than or equal to 1. We will do this through the study of properties of the De Rham cohomology groups of sphere Sn and of compact connected Lie groups. === Fundação de Amparo a P...

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Bibliographic Details
Main Author: Lima, Kennerson Nascimento de Sousa
Other Authors: Guerra, Ediel Azevedo
Format: Others
Language:Portuguese
Published: Universidade Federal de Alagoas 2015
Subjects:
Online Access:http://repositorio.ufal.br/handle/riufal/1042
Description
Summary:We will show that the only connected Euclidean spheres admitting a structure of Lie group are S1 and S3, for all n greater than or equal to 1. We will do this through the study of properties of the De Rham cohomology groups of sphere Sn and of compact connected Lie groups. === Fundação de Amparo a Pesquisa do Estado de Alagoas === Mostraremos que as únicas esferas euclidianas conexas que admitem uma estrutura de grupo de Lie são S1 e S3, para todo n maior ou igual a 1. Faremos isso por intermédio do estudo de propriedades dos grupos de cohomologia de De Rham das esfereas Sn e dos grupos de Lie compactos e conexos.