Introdução às Álgebras de Lie
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)