MTL856: Lie Algebras

3 Credits (3-0-0)

Overlaps with: MTL756

Definitions and examples. Basic concepts. Solvable and Nilpotent Lie algebras, The Engel’s theorem, Lie’s theorem, Cartan’s criterion, Killing form, Finite dimensional semi-simple Lie algebras and their representation theory. The Weyl’s theorem. Representations of sl (2,C). Root space decomposition. Rationality properties. Root systems, The Weyl group. Isomorphism and conjugacy theorems (Cartan subalgebras, Borel subalgebras). Universal enveloping algebras, PBW theorem, Serre’s theorem. Representation theory and characters. Formulas of Weyl, Kostant and Steinberg. Introduction to infinite dimensional Lie algebras.