European Academic Research ISSN 2286-4822
ISSN-L 2286-4822
Impact Factor: 3.4546 (UIF)
DRJI Value : 5.9 (B+)
Article Details :
Article Name :
Symmetric Spaces as Lie Groups and Lie Algebras
Author Name :
UM SALAMA AHMED ABDULLA ALEMAM
Publisher :
Bridge Center
Article URL :
Abstract :
In this paper we have introduced Lie groups and Lie algebras which help to give further understanding of symmetric spaces and help scientists who are seeking for suitable spaces for their applications. One of the aims of this study is to put forward the close connection between different approaches to symmetric spaces namely algebraic and geometrical features of these spaces with some results. We deal with the basic concept of a root system. First, its origins in the theory of Lie algebras are exposed, then an axiomatic definition is provided. So this Paper is an attempt to disclose some of these features and helps in more understanding and put forward a base for future applications.
Keywords :
Manifolds, Tensor Field, Lie groups, Lie algebras, Root systems, Cartan Matrix, Dynkin diagrams, Symmetric spaces.

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