MATH 650: Lie Algebras
Fall 2012
University of
Pennsylvania
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