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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.

Article Information
Editor(s):
(1) Morteza Seddighin, Professor, Indiana University East Richmond, USA.
(2) Dragos-Patru Covei, Professor, Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, Romania.
Reviewers:
(1) Hatice Kusak Samanci, Bitlis Eren University, Turkey.
(2) Xiaolan Liu, Sichuan University of Science & Engineering, China.
(3) Piyush Shroff, Texas State University, USA.
(4) Raul Manuel Falcon Ganfornina, University of Seville, Spain.
(5) Emanuel Guariglia, University of Salerno, Italy.
Complete Peer review History: http://www.sciencedomain.org/review-history/23152

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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