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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