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 :

  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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E-mail: chairman.math[at]iisc[dot]ac[dot]in