Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

MA 315: Lie Algebras and their Representations

Credits: 3:0

LIE ALGEBRAS AND THEIR REPRESENTATIONS

Finite dimensional Lie algebras, Ideals, Homomorphisms, Solvable and Nilpotent Lie algebras, Semisimple Lie algebras, Jordan decomposition, Kiling form, root space decomposition, root systems, classification of complex semisimple Lie algebras Representations Complete reducibility, weight spaces, Weyl character formula, Kostant, steinberg and Freudenthal formulas

Suggested books and references:

1. J E Humphreys, Introduction to Lie algebras and Representation theory, Springer-Verlag, 1972.
2. J P Serre, Complex Semisimple Lie Algebras, Springer, 2001.
3. Fulton. W., and Harris J., Representation theory, Springer-Verlag. 1991.

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