Lecture 1: Manifolds
Lecture 2: Lie Groups I
Lecture 3: Lie Groups II
Lecture 4: Homogeneous Spaces and Lie Group Actions
Problem set 1 due
Lecture 5: Tensor Fields
Lecture 6: Classical Lie Groups
Problem set 2 due
Lecture 7: The Exponential Map of a Lie Group
Lecture 8: Lie Algebras
Problem set 3 due
Lecture 9: Fundamental Theorems of Lie Theory
Lecture 10: Proofs of the Fundamental Theorems of Lie Theory
Problem set 4 due
Lecture 11: Representations of Lie Groups and Lie Algebras
Lecture 12: The Universal Enveloping Algebra of a Lie Algebra
Problem set 5 due
Lecture 13: The Poincare-Birkhoff-Witt Theorem
Lecture 14: Free Lie Algebras and the Baker-Campbell-Hausdor Formula
Problem set 6 due
Lecture 15: Solvable and Nilpotent Lie Algebras and Theorems of Lie and Engel
Lecture 16: Semisimple and Reductive Lie Algebras, the Cartan Criteria
Problem set 7 due
Lecture 17: Proofs of the Cartan Criteria and Properties of Semisimple Lie Algebras
Lecture 18: Extensions of Representations, Whitehead’s Theorem, and Compete Reducibility
Problem set 8 due
Lecture 19: Structure of Semisimple Lie Algebras I
Lecture 20: Structure of Semisimple Lie Algebras II
Problem set 9 due
Lecture 21: Root Systems
Lecture 22: Properties of the Weyl Group
Problem set 10 due
Lecture 23: Dynkin Diagrams
Lecture 24: Construction of a Semisimple Lie Algebra from a Dynkin Diagram
Problem set 11 due
Lecture 25: Representation Theory of Semisimple Lie Algebras
Lecture 26: The Weyl Character Formula
Problem set 12 due
