Lie Algebras: a crash course

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Basics of Lie algebras: Cartan subalgebra and roots. This should be explained with the example of SU(2) and SU(3) [1, chapter 8, 12] Representations of Lie algebras and weights: again this should be explained mainly with the example of SU(2) and SU(3) [1, chaper 11, 12, 13]. Classes of semisimple Lie algebras (Dynkin's classification) [1, chapter 21]. -- [1] W. Fulton, J. Harris, Representation theory, Springer (1991).