The Classification of Semisimple Lie Algebra With Some Applications

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-12
Year of Publication : 2019
Authors : A. G. Dzarma, D. Samaila
  10.14445/22315373/IJMTT-V65I12P520

MLA

MLA Style:A. G. Dzarma, D. Samaila  "The Classification of Semisimple Lie Algebra With Some Applications" International Journal of Mathematics Trends and Technology 65.12 (2019):180-199. 

APA Style: A. G. Dzarma, D. Samaila(2019). The Classification of Semisimple Lie Algebra With Some Applications International Journal of Mathematics Trends and Technology, 180-199.

Abstract
This paper presents the classification of semisimple Lie algebras and its application. Starting on the level of Lie groups, we concisely introduce the connection between Lie groups and Lie algebras. We then further explore the structure of Lie algebras, which we introduced semisimple Lie algebras and their root decomposition. We then turn our study to root systems as separate structures, and finally simple root systems, which can be classified by Dynkin diagrams. Then also considered quantum mechanics and its rotation invariance as its physical application.

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Keywords
Lie algebra, Lie group, root decomposition, root system, Dynkin diagram