# MATH 650: Lie Algebras

Fall 2012

University of
Pennsylvania

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*Basic Information*

Textbook: Introduction to Lie Algebras and Representation
Theory, by James E. Humphreys

Basic Policies

Assignment 1 (Due Oct 2)

Assignment 2 (Due Oct 23)

Assignment 3 (Due Dec 19)

Additional Notes:

Lecture 1 - Basic
Definitions and Examples

Lecture 2 - Engel's Theorem

Lecture 3 - Lie's Theorem

Lecture 4 - Fitting and
Jordan decompositions

Lecture 5 - Cartan's
Criterion and the Killing form

Lecture 6 - Structure of
Semisimple Lie algebras

Lecture 7 -
Complete Reducibility of Representations

Lecture 8 - Preservation of
the Jordan decomposition, and Levi's Theorem

Lecture 9 - Structure of
sl(2,C) modules

Lecture 10 - Examples: so(3)
and sl(2) Representations in Physics and Geometry

Lecture 11 - Maximal Toral
Subalgebras

Lecture 12 - Roots and Root
Spaces I

Lecture 13 - Roots and Root
Spaces II

Lecture 14 - Examples: so(4) and g2

Lecture 15 - Axiomatics

Lecture 16 - Simple Roots

Lecture 17 - The Weyl Group

Lecture 18 - The Classification Thoerem I

Lecture 19 - The Classification Thoerem II

Lecture 20 - Isomorphisms and Automorphisms

Lecture 21 - Isomorphisms and Automorphisms II

Lecture 22 - Cartan and Engel
Subalgebras

Textbook segments:

Table of Contents

Chapter III

References

Index of Terminology

Index of Symbols

Instructor: Brian Weber,
brweber AT math dot upenn dot edu

Office: DRL 4N67

Office Hours: Mon 2-3, Tues
4:30-5:30, Wed 4-5