Introduction to Lie Algebras

Code: MA624 | L-T-P-C: 3-0-0-6

 Prerequisites: MA 521 and MA 522 or equivalent.

Lie algebras and Lie algebra homomorphisms (definition and examples), solvable and nilpotent Lie algebras, Engel's theorem; Semisimple Lie algebras - Lie's theorem, Cartan's criterion, Jordan-Chevalley decomposition, killing form, complete reducibility of representations, Weyl's theorem, irreducible representations of the Lie algebra SL(2), weights and maximal vectors, root space decomposition; Root systems - definition and examples, simple roots and the Weyl group, Cartan matrix of a root system, Dynkin diagrams, classification theorem.

Texts/References:

1. J. E. Humphreys, Introduction to Lie Algebras and Representation theory, Graduate texts in Mathematics, Springer, 1972.
2. W. Fulton and J. Harris, Representation theory - A First Course, Graduate texts in Mathematics, Springer, 1991.
3. K. Erdmann and M. J. Wildon, Introduction to Lie Algebras,Springer Undergraduate Mathematics Series, 2006.
4. B.. C. Hall, Lie Groups, Lie Algebras, and Representations, An Elementary Introduction, Graduate Texts in Mathematics, Springer, 2010.
5. N. Jacobson, Lie Algebras, Courier Dover Publications, 1979.