# Introduction to Lie Algebras

- Institution: IISc Bangalore
- Department: Mathematics
- Teacher: Prof. R Venkatesh
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111108414)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111108414)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lec 01 -An introduction to Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108414/bcd7f4f56d08) (Video)
2. [Lec 02 - Lie subalgebra and Homomorphism](https://invisiblenetwork.ai/learn/nptel/111108414/e77212ea4cd8) (Video)
3. [Lec 03 - Some Problems.](https://invisiblenetwork.ai/learn/nptel/111108414/fa7564693977) (Video)
4. [Lec 04 - Ideals and Quotient algebras.](https://invisiblenetwork.ai/learn/nptel/111108414/27e19ba56f87) (Video)
5. [Lec 05 - Isomorphism theorems](https://invisiblenetwork.ai/learn/nptel/111108414/3954fb57d0ff) (Video)
6. [Lec 06 - Correspondence between ideals](https://invisiblenetwork.ai/learn/nptel/111108414/73a95af58357) (Video)
7. [Lec 07 - Low dimensional Lie algebra-1](https://invisiblenetwork.ai/learn/nptel/111108414/db3625231814) (Video)
8. [Lec 08 - Low dimensional Lie algebra-2.](https://invisiblenetwork.ai/learn/nptel/111108414/3c542a9d7bd9) (Video)
9. [Lec 09 - Some more definitions.](https://invisiblenetwork.ai/learn/nptel/111108414/7c1d403a642c) (Video)
10. [Lec 10 - Solvable and nilpotent Lie algebra.](https://invisiblenetwork.ai/learn/nptel/111108414/4a435ba4a554) (Video)
11. [Lec 11 Nilpotent Lie algebra](https://invisiblenetwork.ai/learn/nptel/111108414/f8be23b0f0a3) (Video)
12. [Lec 12 The invariance Lemma](https://invisiblenetwork.ai/learn/nptel/111108414/58760de37854) (Video)
13. [Lec 13 Engel’s and Lie’s theorem](https://invisiblenetwork.ai/learn/nptel/111108414/39138d83cec0) (Video)
14. [Lec 14 Engel’s and Lie’s theorem (continued)](https://invisiblenetwork.ai/learn/nptel/111108414/8c08a56d9d09) (Video)
15. [Lec 15 Lie’s theorem](https://invisiblenetwork.ai/learn/nptel/111108414/046defce3998) (Video)
16. [Lec 16 Basics of Representation theory.](https://invisiblenetwork.ai/learn/nptel/111108414/e34893dc1570) (Video)
17. [Lec 17 Basics of Representation theory (continued).](https://invisiblenetwork.ai/learn/nptel/111108414/d21dc0eab0f0) (Video)
18. [Lec 18 Schur’s lemma](https://invisiblenetwork.ai/learn/nptel/111108414/d2275bb6544e) (Video)
19. [Lec 19 Finite dimensional representations of of sl2(C).](https://invisiblenetwork.ai/learn/nptel/111108414/177d2fc7d49a) (Video)
20. [Lec 20 Classification of finite dimensional representations of of sl2(C).](https://invisiblenetwork.ai/learn/nptel/111108414/c573643ddcf3) (Video)
21. [Lec 21 Complete reducibility of finite dimensional representation of sl2(C), part 1.](https://invisiblenetwork.ai/learn/nptel/111108414/f19471509b86) (Video)
22. [Lec 22 Complete reducibility of finite dimensional representation of sl2(C), part 2.](https://invisiblenetwork.ai/learn/nptel/111108414/f8fea78d8fb4) (Video)
23. [Lec 23 Applications of Lie’s and Engel’s theorem.](https://invisiblenetwork.ai/learn/nptel/111108414/80792d4dcde9) (Video)
24. [Lec 24 Applications of Weyl’s Theorem for sl2(C).](https://invisiblenetwork.ai/learn/nptel/111108414/df213e76ea99) (Video)
25. [Lec 25 New representations form given representations.](https://invisiblenetwork.ai/learn/nptel/111108414/c96cd787de68) (Video)
26. [Lec 26 Primary decomposition Theorem and Jordan-Chevalley decomposition.](https://invisiblenetwork.ai/learn/nptel/111108414/7465539ece79) (Video)
27. [Lec 27 Cartan’s criteria for solvability.](https://invisiblenetwork.ai/learn/nptel/111108414/b980e507a3bf) (Video)
28. [Lec 28 Cartan’s criteria for semisimplicity and its consequences](https://invisiblenetwork.ai/learn/nptel/111108414/25445627484d) (Video)
29. [Lec 29 Abstract Jordan decomposition in semisimple Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108414/c3d3240aca4f) (Video)
30. [Lec 30 Casimir element of a representation of a semisimple Lie algebra.](https://invisiblenetwork.ai/learn/nptel/111108414/912fc2ad3c5b) (Video)
31. [Lec 31 Weyl’s Theorem of complete reducibility for semisimple Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108414/dc705387603b) (Video)
32. [Lec 32 Root space decomposition of semisimple Lie algebras.](https://invisiblenetwork.ai/learn/nptel/111108414/88ad13557ff1) (Video)
33. [Lec 33 Centralizer of a maximal toral subalgebra.](https://invisiblenetwork.ai/learn/nptel/111108414/5fcfa8472212) (Video)
34. [Lec 34 Properties of roots.](https://invisiblenetwork.ai/learn/nptel/111108414/904dc031c1e7) (Video)
35. [Lec 35 More properties of roots.](https://invisiblenetwork.ai/learn/nptel/111108414/bebebc1b97d6) (Video)
36. [Lec 36 Rationality of roots.](https://invisiblenetwork.ai/learn/nptel/111108414/f6217a9c3bbe) (Video)
37. [Lec 37 Abstract root system and Weyl groups](https://invisiblenetwork.ai/learn/nptel/111108414/488c8b278be1) (Video)
38. [Lec 38 Isomorphism of Root systems and dual root systems](https://invisiblenetwork.ai/learn/nptel/111108414/457d49978e9c) (Video)
39. [Lec 39 Root systems of Ranks 1 and 2](https://invisiblenetwork.ai/learn/nptel/111108414/f0b3a748be1c) (Video)
40. [Lec 40 Classification of rank 2 root systems](https://invisiblenetwork.ai/learn/nptel/111108414/dbf05aa89f55) (Video)
41. [Lec 41 Base of a root system](https://invisiblenetwork.ai/learn/nptel/111108414/bb64123c4dc9) (Video)
42. [Lec 42 Classification of bases](https://invisiblenetwork.ai/learn/nptel/111108414/f4e92cb6af35) (Video)
43. [Lec 43 Basic properties of simple roots](https://invisiblenetwork.ai/learn/nptel/111108414/cac3e1c15b21) (Video)
44. [Lec 44 Characterization of length function](https://invisiblenetwork.ai/learn/nptel/111108414/57f3f6984c28) (Video)
45. [Lec 45 Decomposition of root systems](https://invisiblenetwork.ai/learn/nptel/111108414/7666b4baee8f) (Video)
46. [Lec 46 Root lengths, Cartan Matrices](https://invisiblenetwork.ai/learn/nptel/111108414/7b4371a469f6) (Video)
47. [Lec 47 Cartan matrices and Dynkin diagrams](https://invisiblenetwork.ai/learn/nptel/111108414/f0dfc0c3a3b8) (Video)
48. [Lec 48 Classification of Root systems](https://invisiblenetwork.ai/learn/nptel/111108414/381842eca966) (Video)
49. [Lec 49 Classification of Root systems - Continued](https://invisiblenetwork.ai/learn/nptel/111108414/bd2a15b66d3b) (Video)
50. [Lec 50 Concrete description of root systems](https://invisiblenetwork.ai/learn/nptel/111108414/3720ab60ec24) (Video)
51. [Lec 51 Uniqueness of root systems](https://invisiblenetwork.ai/learn/nptel/111108414/da3c6b3db62c) (Video)
52. [Lec 52 Isomorphism theorem](https://invisiblenetwork.ai/learn/nptel/111108414/206df20cb8cd) (Video)
53. [Lec 53 Isomorphism theorem - continued](https://invisiblenetwork.ai/learn/nptel/111108414/2063f933f0b4) (Video)
54. [Lec 54 Generators and relations](https://invisiblenetwork.ai/learn/nptel/111108414/bb80d4ea1428) (Video)
55. [Lec 55 Serre presentation](https://invisiblenetwork.ai/learn/nptel/111108414/662f15369c04) (Video)
56. [Live Session 14-03-2024](https://invisiblenetwork.ai/learn/nptel/111108414/bcd7f4f56d08-2) (Video)
57. [Live Session 17-03-2025](https://invisiblenetwork.ai/learn/nptel/111108414/e77212ea4cd8-2) (Video)
58. [Live Session 15-04-2025](https://invisiblenetwork.ai/learn/nptel/111108414/fa7564693977-2) (Video)