Математика16 лекций
Представления конечномерных и бесконечномерных алгебр Ли
2023
лекции
Механико-математический факультет
Математика
спецкурс
Преподаватель
Видеолекции
Материалы
О курсе
1:29:11Лекция 1. Solvable and Nilpotent Lie algebras
1:25:09Лекция 2. Solvable and Nilpotent Lie algebras. Continuation
1:34:30Лекция 3. Semisimple Lie algebra
1:21:57Лекция 4. Invariant bilinear forms
1:33:50Лекция 5. Semisimple Lie algebras
1:34:38Лекция 6. Generalization for any semisimple Lie algebra
1:31:33Лекция 7. Root decomposition. Abstract root system
1:26:41Лекция 8. Continuation of the previous lecture. Classification of root systems
1:30:54Лекция 9. Weyl chambers and simple reflections
1:57:43Лекция 10. Classification of root systems. Serre's relations and Serre's theorem
1:41:39Лекция 11. Weight subspaces, representations of highest weight, Verma modules
1:39:10Лекция 12. Classification of finite-dimensional representations of semisimple Lie algebras
1:49:40Лекция 13. Integrable representations. Characters of representations
1:20:21Лекция 14. Young tableaux and representations of gl(n)
1:41:48Лекция 15. Brief introduction to Kac-Moody Lie algebras
1:28:58Лекция 16. Affine Lie algebras
2025 МГУ имени М.В. Ломоносова