Lecture Notes · Lecture Notes
MIT OpenCourseWare
Lie Groups and Lie Algebras I
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. Pavel Etingof
- Term
- Fall 2020
- Level
- Graduate
- What's inside
- 28 other files · 3 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.745 Lie Groups and Lie Algebras I, Fall 2020, Prof. Pavel Etingof — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.
Not included here
5 items from the source could not be safely included:
- MIT's page format for this item wasn't recognized clearly enough to place it safely. (5 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Problem Sets
Course outline
Lecture Notes · Lecture Notes
18.745 F20 Lecture 02: Lie Groups I
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18.745 F20 Lecture 03: Lie Groups II
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18.745 F20 Lecture 04: Homogeneous Spaces and Lie Group Actions
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18.745 F20 Lecture 05: Tensor Fields
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18.745 F20 Lecture 06: Classical Lie Groups
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18.745 F20 Lecture 07: The Exponential Map of a Lie Group
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18.745 F20 Lecture 08: Lie Algebras
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18.745 F20 Lecture 09: Fundamental Theorems of Lie Theory
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18.745 F20 Lecture 10: Proofs of the Fundamental Theorems of Lie Theory
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18.745 F20 Lecture 11: Representations of Lie Groups and Lie Algebras
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18.745 F20 Lecture 12: The Universal Enveloping Algebra of a Lie Algebra
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18.745 F20 Lecture 13: The Poincare-Birkhoff-Witt Theorem
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18.745 F20 Lecture 14: Free Lie Algebras and the Baker-Campbell-Hausdorff Formula
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18.745 F20 Lecture 15: Solvable and Nilpotent Lie Algebras and Theorems of Lie and Engel
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18.745 F20 Lecture 16: Semisimple and Reductive Lie Algebras, the Cartan Criteria
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18.745 F20 Lecture 17: Proofs of the Cartan Criteria and Properties of Semisimple Lie Algebras
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18.745 F20 Lecture 18: Extensions of Representations, Whitehead's Theorem, and Complete Reducibility
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18.745 F20 Lecture 19: Structure of Semisimple Lie Algebras I
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18.745 F20 Lecture 20: Structure of Semisimple Lie Algebras II
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18.745 F20 Lecture 21: Root Systems
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18.745 F20 Lecture 22: Properties of the Weyl Group
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18.745 F20 Lecture 23: Dynkin Diagrams
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18.745 F20 Lecture 24: Construction of a Semisimple Lie Algebra from a Dynkin Diagrams
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18.745 F20 Lecture 25: Representation Theory of Semisimple Lie Algebras
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18.745 F20 Lecture 26: The Weyl Character Formula
MIT OpenCourseWare, Prof. Pavel Etingof, 18.745 Lie Groups and Lie Algebras I, Fall 2020.
License: CC BY-NC-SA 4.0 · Edition: Fall 2020 · Open the original course on OCW ↗
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