We will go over the basics of structure and representation theory of finite dimensional complex Lie algebras. We will define basic concepts as ideals, homomorphisms, representations, etc. Then we will move to structure theory of semisimple Lie algebras: Killing form, Casimir elements, root systems, classification of simple algebras. And finally we will go to the basics of representation theory: characters, Weyl formulas, etc. Even though we will try to keep it purely algebraic (1) and we may mention some connections to Lie Group theory and geometry (2).
The only previous knowledge that this class will assume is some familiarity with basic algebraic objects like rings and fields. Understanding the notion of manifold would be useful when making connections to Lie Group theory.
(1) HUMPHREYS, J.E. - Introduction to Lie algebras and representation theory" (Springer)
(2) KNAPP'S, A. W. - Lie groups beyond an introduction" (Birkhäuser).
Aula 11 - 27.01.2011 - download
Aula 12 - 31.01.2011 - download
Aula 13 - 01.02.2011 - download
Aula 14 - 03.02.2011 - download
Aula 15 - 14.02.2011 - download
Aula 16 - 16.02.2011 - download