Complex simple Lie algebras classification

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SUMMARY

The discussion focuses on the classification of complex simple Lie algebras, specifically the simple groups An, Bn, Cn, Dn, and the exceptional groups E, F, G. Participants seek comprehensive resources to understand these algebras and their representation through Coxeter–Dynkin diagrams. A recommended resource is R. Gilmore's book, “Lie Groups, Lie Algebras, and Some of their Applications,” published by John Wiley & Sons in 1974, which provides valuable insights into these topics.

PREREQUISITES
  • Understanding of Lie algebras and their classifications
  • Familiarity with Coxeter–Dynkin diagrams
  • Basic knowledge of group theory
  • Experience with mathematical literature and terminology
NEXT STEPS
  • Research the classification of complex simple Lie algebras in detail
  • Study Coxeter–Dynkin diagrams and their applications in representation theory
  • Explore advanced texts on Lie groups and algebras
  • Investigate contemporary resources and articles on Lie algebra applications
USEFUL FOR

This discussion is beneficial for mathematicians, theoretical physicists, and students specializing in algebra, particularly those interested in the classification and application of complex simple Lie algebras.

Reperio
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Does anybody can propose a good book on classification of the complex simple Lie algebras. I know that they fall into several simple (An, Bn, Cn, Dn) and exceptional groups (E, F, G), but I find only a pieces of information about these algebras.
Also, they could be represented by Coxeter–Dynkin diagram. In simples words, what are they and how to get an intuition to read them?

Good article or book about these diagrams and groups will be hellpfull...

Thank you
 
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Reperio said:
Good article or book about these diagrams and groups will be hellpfull...

R.Gilmore, “Lie Groups,Lie Algebras,and Some of their Applications”, John Wiley&Sons, 1974

Regards, Dany.
 

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