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Browse materialsMIT 18.755 · Spring 2024

Lie Groups and Lie Algebras II

Subjects: Algebra · Mathematics

Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain

Instructor: Prof. Pavel Etingof
Term: Spring 2024
Level: Graduate
What's inside: 26 other files · 3 web pages
Materials open: MIT OCW

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Source: MIT OpenCourseWare 18.755 Lie Groups and Lie Algebras II, Spring 2024, 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.

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Lie Groups and Lie AlgebrasPDF Download

MIT OpenCourseWare, Prof. Pavel Etingof, 18.755 Lie Groups and Lie Algebras II, Spring 2024.

License: CC BY-NC-SA 4.0 · Edition: Spring 2024 · Open the original course on OCW ↗

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Lie Groups and Lie Algebras II

Before you start

What's here, and what isn't

Not included here

Materials by section

Syllabus

18.755 S24 Lecture 01: Representations of GLn, I

18.755 S24 Lecture 02: Representations of GLn, II

18.755 S24 Lecture 03: Representations of GLn, III

18.755 S24 Lecture 04: Fundamental and Minuscule Weights

18.755 S24 Lecture 05: Fundamental Representations of Classical Lie Algebras

18.755 S24 Lecture 06: Maximal Root, Exponents, Coxeter Numbers, Dual Representations

18.755 S24 Lecture 07: Differential Forms, Partitions of Unity

18.755 S24 Lecture 08: Integration on Manifolds

18.755 S24 Lecture 09: Representations of Compact Lie Groups

18.755 S24 Lecture 10: Proof of the Peter-Weyl Theorem

18.755 S24 Lecture 11: Representations of Compact Topological Groups

18.755 S24 Lecture 12: The Hydrogen Atom, I

18.755 S24 Lecture 13: The Hydrogen Atom, II

18.755 S24 Lecture 14: Forms of Semisimple Lie Algebras over an Arbitrary Field

18.755 S24 Lecture 15: Classification of Real Forms of Semisimple Lie Algebras

18.755 S24 Lecture 16: Real Forms of Exceptional Lie Algebras

18.755 S24 Lecture 17: Classification of Connected Compact and Complex Reductive Groups

18.755 S24 Lecture 18: Maximal Tori in Compact Groups, Cartan Decomposition

18.755 S24 Lecture 19: Topology of Lie Groups and Homogeneous Spaces, I

18.755 S24 Lecture 20: Topology of Lie Groups and Homogeneous Spaces, II

18.755 S24 Lecture 21: Topology of Lie Groups and Homogeneous Spaces, III

18.755 S24 Lecture 22: Levi Decomposition

18.755 S24 Lecture 23: The Third Fundamental Theorem of Lie Theory

18.755 S24 Lecture 24: Ado's Theorem

18.755 S24 Lecture 25: Borel Subgroups and the Flag Manifold of a Complex Reductive Lie Group