A Discussion on Some Topological and Algebraic Features of Symmetric Spaces
DOI:
https://doi.org/10.9734/bpi/mcscd/v10/3301Keywords:
Topological spaces, metric spaces, topological manifold, riemannian manifold, lie groups, lie algebras, root systems, homogeneous spaces, symmetric spacesAbstract
Many scientific problems in various fields may have their own conditions that might not agree with the geometric structure and properties of some spaces familiar to mathematicians and geometers. Many properties of symmetric spaces can be studied through their Lie algebras and root systems, and especially the problem of classification of symmetric spaces.
This study introduced some approaches, geometrical and algebraic, which help to give a further understanding of symmetric spaces. Symmetric space is a very important field for understanding abstract and applied features of spaces. This study also introduced Riemannian Manifold, Lie groups and Lie algebras, and some of their topological and algebraic properties, with some concentration on Lie algebras and root systems, which help classification and many applications of symmetric spaces. The paper is an attempt to explain some algebraic features of symmetric spaces and how to get some of their properties using an algebraic approach, concluded with some results.
