# MATH 651: Lie Algebras

Spring 2013

University of
Pennsylvania

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*Basic Information*

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

Supplemental Text: *Lie Algebras*, Nathan Jacobson

Assignment 1 (Due: Feb 25)

Assignment 2 (Due: Mar 15)

Assignment 3 (Due: Apr 12)

Assignment 4 (Due: May 7)

Textbook Segment: Humphreys Ch13

Additional Notes:

Lecture 1 - Groups and
Algebras

Lecture 2 - Examples

Lecture 3 - Campbell-Baker-Hausdorff

Lecture 4 - Lie Algebra
Cohomology I

Lecture 5 - Lie Algebra
Cohomology II

Lecture 6 - Lie Algebra
Cohomology III

Lecture 7 - Universal Enveloping
Algebras and Related Concepts I

Lecture 8 - Universal
Enveloping Algebras and Related Concepts II

Lecture 9 - Representation Theory I: Examples

Lecture 10 - Representation Theory II: Heuristics

Lecture 11 - Representation Theory III: Theory of Weights

Lecture 12 - Representation Theory IV: Existence

Lecture 13 - Characters

Lecture 14 - The Harish-Chandra Isomosrphism

Special Lecture - The Octonions

Lecture 15 - Odds and Ends

Lecture 16 - The Weyl Dimension Formula I

Lecture 17 - The Weyl Dimension Formula II

Lecture 18 - Clifford Algebras and Spin Groups

Lecture 19 - Clifford and Spin Representations

Lecture 20 - Duality and Triality

Lecture 21 - Jordan Algebras and Projective Spaces

Lecture 22 - F_4

Lecture 23 - The Magic Square

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