NOC:Introduction to Lie Algebras

Lecture 1 - An Introduction to Lie Algebras

Lecture 2 - Lie subalgebra and Homomorphism

Lecture 3 - Some Problems

Lecture 4 - Ideals and Quotient algebras

Lecture 5 - Isomorphism theorems

Lecture 6 - Correspondence between ideals

Lecture 7 - Low dimensional Lie algebra - 1

Lecture 8 - Low dimensional Lie algebra - 2

Lecture 9 - Some more definitions

Lecture 10 - Solvable and nilpotent Lie algebra

Lecture 11 - Nilpotent Lie algebra

Lecture 12 - The invariance Lemma

Lecture 13 - Engel's and Lie's Theorem

Lecture 14 - Engel's and Lie's Theorem (Continued...)

Lecture 15 - Lie's Theorem

Lecture 16 - Basics of Representation Theory

Lecture 17 - Basics of Representation Theory (Continued...)

Lecture 18 - Schur's lemma

Lecture 19 - Finite dimensional representations of of sl2(C)

Lecture 20 - Classification of finite dimensional representations of sl2(C)

Lecture 21 - Complete reducibility of finite dimensional representation of sl2(C) - Part 1

Lecture 22 - Complete reducibility of finite dimensional representation of sl2(C) - Part 2

Lecture 23 - Applications of Lie's and Engel's theorem

Lecture 24 - Applications of Weyl's Theorem for sl2(C)

Lecture 25 - New representations form given representations

Lecture 26 - Primary decomposition Theorem and Jordan-Chevalley decomposition

Lecture 27 - Cartan's criteria for solvability

Lecture 28 - Cartan's criteria for semisimplicity and its consequences

Lecture 29 - Abstract Jordan decomposition in semisimple Lie algebras

Lecture 30 - Casimir element of a representation of a semisimple Lie algebra

Lecture 31 - Weyl's Theorem of complete reducibility for semisimple Lie algebras

Lecture 32 - Root space decomposition of semisimple Lie algebras

Lecture 33 - Centralizer of a maximal toral subalgebra

Lecture 34 - Properties of roots

Lecture 35 - More properties of roots

Lecture 36 - Rationality of roots

Lecture 37 - Abstract root system and Weyl groups

Lecture 38 - Isomorphism of Root systems and dual root systems

Lecture 39 - Root systems of Ranks 1 and 2

Lecture 40 - Classification of rank 2 root systems

Lecture 41 - Base of a root system

Lecture 42 - Classification of bases

Lecture 43 - Basic properties of simple roots

Lecture 44 - Characterization of length function

Lecture 45 - Decomposition of root systems

Lecture 46 - Root lengths, Cartan Matrices

Lecture 47 - Cartan matrices and Dynkin diagrams

Lecture 48 - Classification of Root systems

Lecture 49 - Classification of Root systems (Continued...)

Lecture 50 - Concrete description of root systems

Lecture 51 - Uniqueness of root systems

Lecture 52 - Isomorphism theorem

Lecture 53 - Isomorphism theorem (Continued...)

Lecture 54 - Generators and relations

Lecture 55 - Serre presentation