Apolo

Atividade

99927 - Introduction to Lie algebras

Período da turma:

01/02/2021 a 12/02/2021

Selecione um horário para exibir no calendário:

Descrição:

Aula 1

Introduction
- Symmetries and groups
- Lie algebras as linear approximations of groups
- Some examples
2. Beginnings
- Definitions
- Solvable, Simple and Nilpotent algebras.

Aula 2
1. Solvable Lie algebras and Lie theorem
2. Nilpotent Lie algebras and Engel’s Theorem

Aula 3
1. Killing Form and Cartan semsimplicity Criteria
2. Jordans canonical form (without proof)

Aula 4
1. Weights and generalized weights spaces
2. Weight space decomposition
3. Cartan subalgebras
4. Sketch the proof of existence of Cartan Subalgebras for complex semisimple Lie algebras. 5. Cartan subalgebras are unique (without proof)

Aula 5
1. Roots
2. Root systems and SL(2,C)
3. Abstract root systems and irreducibility

Aula 6
1. Cartan matrix
2. Dynkin diagram
3. Weyl Group

Bibliografia:

[1] A. Knapp, Lie Groups beyond an introduction. Progress in Mathematics, 140, Birkhäuser Basel, 2002.
[2] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, 1978.
[3] J. Humphreys, Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, 9, Springer-Verlag New York, 1978

Carga Horária:

12 horas

Tipo:

Obrigatória

Vagas oferecidas:

300

Ministrantes:

Uirá Norberto Matos de Almeida

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