Представления конечномерных и бесконечномерных алгебр Ли. Семинары
Математика
12 лекций
2023
семинары
Механико-математический факультет
Математика
спецкурс
Преподаватель
- 01:15:43Семинар 1. The commutator, nilpotency, and solvability
- 01:29:09Семинар 2. Nilpotency, simplicity and reductiveness
- 01:14:28Семинар 3. Bilinear forms and Killing form
- 01:18:51Семинар 4. Semisimple Lie algebras
- 01:20:27Семинар 5. Cartan subalgebra and root decomposition
- 01:33:33Семинар 6. Cartan subalgebra and abstract root system
- 01:27:48Семинар 7. Abstract and Euclidean root systems
- 01:34:27Семинар 8. Weyl chambers and simple reflections
- 01:06:43Семинар 9. Classification of root systems. Serre's relations and Serre's theorem
- 01:18:43Семинар 10. Weight subspaces, representations of highest weight, Verma modules
- 01:06:35Семинар 11. Classification of finite-dimensional representations of semisimple Lie algebras
- 01:27:51Семинар 12. Young tableaux and representations of gl(n)