Math 8272: Lie Groups and Lie Algebras

COURSE SYLLABUS

Spring 2016

CLASS MEETINGS: MWF 9:05-9:55 (VinH 209; new room!)

INSTRUCTOR: Sasha Voronov

OFFICE: VinH 324

PHONE: (612) 624-0355

E-MAIL ADDRESS: voronov@umn.edu. You are welcome to use e-mail to send questions to me.

INTERNET: All class announcements and assignments will be posted on the class homepage http://www.math.umn.edu/~voronov/8272/index.html and NOT handed out in class.

OFFICE HOURS: Mon 11:15-12:05, Wed 10:10-11:00, Fri 10:10-11:00, or by appointment.

TEXT:  An introduction to Lie groups and Lie algebras, 1st edition, 2008, by Alexander Kirillov, Jr. Available for purchase at the bookstore and online, and for free electronically through the library. There is also a hard copy on reserve at the Math Library. A list of Errata is posted on the class web page.

CONTENT: In the Fall semester, we covered the first five chapters of the textbook, including the following topics: definitions and basic properties of Lie groups and Lie algebras; classical matrix Lie groups; Lie subgroups and their corresponding Lie subalgebras; covering groups; the exponential map; correspondence between Lie algebras and simply connected Lie groups; Baker-Campbell-Hausdorff formula; homogeneous spaces; solvable and nilpotent Lie algebras; Lie's and Engels's theorems; semisimple Lie algebras; and Levi decomposition. In the Spring semester, we will cover Chapters 6-8, including complex semisimple Lie algebras and their representation theory; cohomology of Lie algebras; root systems. We will also cover Maurer-Cartan forms.

PREREQUISITES: The prerequisite is Math 8271, the first semester of this course.

GETTING HELP:

REQUIREMENTS: : There will be homeworks every other week, but no exams.

GRADING: Based on your homework. Class participation may be taken into account. Grades will be assigned on curve. I expect you to put enough hard work to earn grades not lower than a B. The curve does not exclude the possibility of everybody getting A's, though, but this happens rather rarely.

IMPORTANT DATES:

January 20: First class meeting.

March 14-18: Spring Break.

March 21: I am out of the country at a workshop (extension of Spring Break for you).

May 6: Last class meeting.

Page created on 01/19/2016, office hours updated on 02/01/2016.