MATH 651: Lie Algebras
Spring 2013
University of
Pennsylvania
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