|
Description
The course is an introduction to Lie groups and Lie algebras with an emphasis on the structure and classification of compact connected Lie groups as well as their basic representation theory. Prerequisites: A theoretical linear algebra course. Background in topology and differential geometry at introductory graduate level is strongly encouraged. |
|
Announcements
o Sep. 25: HW1 posted (below). o Oct. 26: The book Quantum Theory, Groups and Representations: An Introduction by Peter Woit is great to learn about connections with physics and quantum mechanics. To start look at Sections 2 and 3. By the way, Peter Woit has a popular blog on physics and math. o Oct. 29: HW2 posted. o Oct. 31: The book Group Theoretical Aspects of Quantum Mechanics by Jose Alvarado is also a nice introductory book about representation theory and quantum physics. o Nov 19: HW2 due date extended to Monday after Thanksgiving. o Nov 27: Typo in HW2 corrected. Problem 2 it should be SU(n+1). o Dec. 1: HW3 posted. It is shorter than the previous ones. |
|
Homeworks and other online material
Homework 1 Homework 2 Homework 3 Take-home final exam |
|
Course Information
o Time: MW 3:00PM - 4:15PM o Location: Thackeray 627 o There will 3 homework and a final exam. o Office hours: By appointment, I am usually in my office on MWF. o Text: Brocker and Tom Dieck “Representations of compact Lie groups” o Some other books on Lie groups (I have not looked carefully at all of these books myself, pdf files of some of them are available for download through Pitt library): - Fulton and Harris, “Representation theory, a first course” - Bump, “Lie groups” - Hall, “Lie groups, Lie algebras and representations” - Sepanski, “Compact Lie groups” - Kosmann, “Groups and symmetries” - Hilger and Neeb, “Structure and geometry of Lie groups” For manifolds and Lie groups: - Warner, “Foundations of Differentiable Manifolds and Lie Groups” |
|
Instructor's
Information
Email: kavehk AT pitt.edu Office: Thackeray #424 Office hours: by appointment, I am usually in MWF most of the day. Office phone: 412-624-8331 |