Titlebook: Algebra 4; Lie Algebras, Cheval Ramji Lal Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springe

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Horst Treiblmaier,Hans Robert HansenThe structure theory of semi-simple Lie algebras, Geometry of root systems, Dynkin diagrams, classification of semi-simple Lie algebras, Existence theorem, the Theorem of Serre, and the isomorphism theorem constitute the subject matter of this chapter.

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Lie Algebras,In this chapter, we develop the basic language of Lie algebras including universal enveloping algebras (PBW theorem), free Lie algebras, solvable, nilpotent, and semi-simple Lie algebras. We also establish the theorem of Weyl about the complete reducibility of representations of semi-simple Lie algebras.