Sobre a topologia do grupo ortogonal generalizado

Abstract

In this work we present a description of the Generalized Orthogonal Group and develop a study on some of its topological aspects such as compactness, connectedness and fundamental group. These results are obtained by applying Mostow s Decomposition Theorem, a more refined version of Gl(n, C) polar decomposition. Bearing these goals in mind, we build the foundations starting with a simple approach involving algebra, geometry and topology in the study of topological groups, matrix Lie groups and Lie algebras.