Список всех тем лекций

Лекция 1. Solvable and Nilpotent Lie algebras.
Organization issues Solvable and Nilpotent Lie algebras

Лекция 2. Solvable and Nilpotent Lie algebras. Continuation.
Proof of a g solvability Corollary Examples Lie's Theorem Corollary Apply Lie's theorem to adjoint representation of g Lemma Engel's theorem Corollary (Second Engel's theorem)

Лекция 3. Semisimple Lie algebra.
Definitions Proposition of semisimplicity Lemma Proposition of a unique maximal solvable ideal Theorem Theorem about radical (Levi's decomposition) Example

Лекция 4. Invariant bilinear forms.
Definition of invariant bilinear form Theorem Theorem (Cartan's criteria of semisimplicity) The first proof of proposition The second proof of proposition Claim Proof of Lemma

Лекция 5. Semisimple Lie algebras.

Лекция 6. Generalization for any semisimple Lie algebra.

Лекция 7. Root decomposition. Abstract root system.

Лекция 8. Continuation of the previous lecture. Classification of root systems.

Лекция 9. Weyl chambers and simple reflections.

Лекция 10. Classification of root systems. Serre's relations and Serre's theorem.

Лекция 11. Weight subspaces, representations of highest weight, Verma modules.

Лекция 12. Classification of finite-dimensional representations of semisimple Lie algebras.

Лекция 13. Integrable representations. Characters of representations.

Лекция 14. Young tableaux and representations of gl(n).

Лекция 15. Brief introduction to Kac-Moody Lie algebras.

Лекция 16. Affine Lie algebras.