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/8271/index.html and NOT handed out in class.
OFFICE HOURS: Mon 11:15-12:05, Wed 11:15-12:05, 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.
CONTENT: In the Fall semester, we will cover 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; Maurer-Cartan forms; exponential map; correspondence between Lie algebras and simply connected Lie groups; Baker-Campbell-Hausdorff formula; homogeneous spaces.
PREREQUISITES: The official prerequisite is Math 8302 (Manifolds and Topology I) or equivalent. In reality, you need to be familiar with the basics of topology and differential geometry (manifolds, vector fields, differential forms, fundamental groups, covering spaces) and basic algebra (rings, modules). Familiarity with exact sequences will also help.
GETTING HELP:
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:
September 14: First class meeting.
October 31: Halloween.
November 26-27: Thanksgiving holiday.
December 16: Last class meeting.
Page created on 09/04/2015; office hours modified on 09/23/2015