Programa de Doutorado 2011: Introduction to Lie Algebras

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.

Referências:
(1) HUMPHREYS, J.E. - Introduction to Lie algebras and representation theory" (Springer) 
(2) KNAPP'S, A. W. - Lie groups beyond an introduction" (Birkhäuser).

 

Vídeos
Reimundo Heluani

Aula 01 - 03.01.2011 - parte 1 | parte 2

Aula 02 - 04.01.2011 - parte 1 | parte 2

Aula 03 - 06.01.2011 - parte 1 | parte 2

Aula 04 - 10.01.2011 - parte 1 | parte 2

Aula 05 - 11.01.2011 - parte 1 | parte 2

Aula 06 - 13.01.2011 - parte 1 | parte 2

Aula 07 - 17.01.2011 - parte 1 | parte 2

Aula 08 - 18.01.2011 - parte 1 | parte 2

Aula 09 - 24.01.2011 - parte 1 | parte 2

Aula 10 - 25.01.2011 - parte 1 | parte 2

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

Aula 17 - 17.02.2011 - parte 1 | parte 2

Aula 18 - 21.02.2011 - parte 1 | parte 2

Aula 19 - 22.02.2011 - parte 1 | parte 2

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