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Journal of Advances in Mathematics and Computer Science

Journal of Advances in Mathematics and Computer Science, ISSN: 2456-9968, ISSN: 2231-0851 (Past),Vol.: 26, Issue.: 3

 

Review Article

 

Root Systems, Cartan Matrix and Dynkin Diagrams in Classification of Lie Algebras

 

 

Um Salama Ahmed Abdulla Alemam1 and Mohamed Alamin Abdalla Hamid Ahmed1,2*

1Department of Mathematics, Faculty of Education, Alzaiem Alazhari University, Sudan.

2Department of Mathematics, Faculty of Science and Arts - Khulais, University of Jeddah, Saudi Arabia.

 

Abstracts

 

This review paper deals with Lie algebras, with some concentration on root systems, which help in classification and many applications of symmetric spaces. 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.  Bases, Weyl groups,  and the  transitive  action  of  the  latter  on  the  former  are  explained. Finally, the Cartan matrix and Dynkin diagram are exposed to suggest the multiple applications of root systems to other fields of study and  their classification.

 

Keywords :

Lie algebras; Root systems; Weyl group; Cartan Matrix and Dynkin   diagrams.

 

Full Article - PDF    Page 1-10    Article Metrics

 

DOI : 10.9734/JAMCS/2018/38568

Review History    Comments

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