Definitions and Examples, Derivations, Ideals, Homomorphisms, Nilpotent Lie Algebras and Engel’s theorem, Solvable Lie Algebras and Lie’s theorem, Jordan decomposition and Cartan’s criterion, Semisimple Lie algebras, Casimir operator and Weyl’s theorem, Representations of sl(2, F ), Root space decomposition, Abstract root systems, Weyl group and Weyl chambers, Classification of irreducible root systems, Abstract theory of weights, Isomorphism and conjugacy theorems, Universal enveloping algebras and PBW theorem, Representation theory of semi-simple Lie algebras, Verma modules and Weyl character formula.
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- K. Erdmann, M. J. Wildon, “Introduction to Lie Algebras”, Springer Undergraduate Mathematics Series, Springer-Verlag, 2006.
- J.-P. Serre, “Complex Semisimple Lie Algebras”, Springer Monographs in Mathematics, Springer-Verlag, 2001.
- N. Jacobson, “Lie Algebras”, Dover Publications, 1979.