Представления конечномерных и бесконечномерных алгебр Ли
Математика
16 лекций
2023
лекции
Механико-математический факультет
Математика
спецкурс
Преподаватель
- 01:29:11Лекция 1. Solvable and Nilpotent Lie algebras
- 01:25:09Лекция 2. Solvable and Nilpotent Lie algebras. Continuation
- 01:34:30Лекция 3. Semisimple Lie algebra
- 01:21:57Лекция 4. Invariant bilinear forms
- 01:33:50Лекция 5. Semisimple Lie algebras
- 01:34:38Лекция 6. Generalization for any semisimple Lie algebra
- 01:31:33Лекция 7. Root decomposition. Abstract root system
- 01:26:41Лекция 8. Continuation of the previous lecture. Classification of root systems
- 01:30:54Лекция 9. Weyl chambers and simple reflections
- 01:57:43Лекция 10. Classification of root systems. Serre's relations and Serre's theorem
- 01:41:39Лекция 11. Weight subspaces, representations of highest weight, Verma modules
- 01:39:10Лекция 12. Classification of finite-dimensional representations of semisimple Lie algebras
- 01:49:40Лекция 13. Integrable representations. Characters of representations
- 01:20:21Лекция 14. Young tableaux and representations of gl(n)
- 01:41:48Лекция 15. Brief introduction to Kac-Moody Lie algebras
- 01:28:58Лекция 16. Affine Lie algebras