18.745 | Fall 2020 | Graduate

Lie Groups and Lie Algebras I

Lecture Notes

pdf
455 kB
18.745 F20 Lecture 01: Manifolds
pdf
323 kB
18.745 F20 Lecture 02: Lie Groups I
pdf
371 kB
18.745 F20 Lecture 03: Lie Groups II
pdf
377 kB
18.745 F20 Lecture 04: Homogeneous Spaces and Lie Group Actions
pdf
364 kB
18.745 F20 Lecture 05: Tensor Fields
pdf
348 kB
18.745 F20 Lecture 06: Classical Lie Groups
pdf
380 kB
18.745 F20 Lecture 07: The Exponential Map of a Lie Group
pdf
377 kB
18.745 F20 Lecture 08: Lie Algebras
pdf
390 kB
18.745 F20 Lecture 09: Fundamental Theorems of Lie Theory
pdf
343 kB
18.745 F20 Lecture 10: Proofs of the Fundamental Theorems of Lie Theory
pdf
399 kB
18.745 F20 Lecture 11: Representations of Lie Groups and Lie Algebras
pdf
337 kB
18.745 F20 Lecture 12: The Universal Enveloping Algebra of a Lie Algebra
pdf
395 kB
18.745 F20 Lecture 13: The Poincare-Birkhoff-Witt Theorem
pdf
349 kB
18.745 F20 Lecture 14: Free Lie Algebras and the Baker-Campbell-Hausdorff Formula
pdf
339 kB
18.745 F20 Lecture 15: Solvable and Nilpotent Lie Algebras and Theorems of Lie and Engel
pdf
347 kB
18.745 F20 Lecture 16: Semisimple and Reductive Lie Algebras, the Cartan Criteria
pdf
338 kB
18.745 F20 Lecture 17: Proofs of the Cartan Criteria and Properties of Semisimple Lie Algebras
pdf
354 kB
18.745 F20 Lecture 18: Extensions of Representations, Whitehead's Theorem, and Complete Reducibility
pdf
371 kB
18.745 F20 Lecture 19: Structure of Semisimple Lie Algebras I
pdf
337 kB
18.745 F20 Lecture 20: Structure of Semisimple Lie Algebras II
pdf
377 kB
18.745 F20 Lecture 21: Root Systems
pdf
352 kB
18.745 F20 Lecture 22: Properties of the Weyl Group
pdf
420 kB
18.745 F20 Lecture 23: Dynkin Diagrams
pdf
365 kB
18.745 F20 Lecture 24: Construction of a Semisimple Lie Algebra from a Dynkin Diagrams
pdf
368 kB
18.745 F20 Lecture 25: Representation Theory of Semisimple Lie Algebras
pdf
408 kB
18.745 F20 Lecture 26: The Weyl Character Formula

Course Info

Instructor

Departments

As Taught In

Fall 2020

Level

Graduate

Topics

Learning Resource Types

Lecture Notes
Open Textbooks
Problem Sets
Download Course
MIT Open Learning
Over 2,500 courses & materials
Freely sharing knowledge with learners and educators around the world. Learn more
© 2001–2026 Massachusetts Institute of Technology
Accessibility
Creative Commons License
Terms and Conditions
Proud member of:
© 2001–2026 Massachusetts Institute of Technology