Lie groups and Lie algebras (MATH 224b, Spring 2015)



Day & Time: Tuesday and Friday 11:30am — 12:45

Location: Goldsmith 0226

Instructor: Joel Bellaiche

Office hours:TBA

Grade: 30% exercises in class, 30% personal project, 40% final exam

Textbooks:

  • Lang: Algebra
  • Serre: Representation of finite groups.

    Program:

  • Non-Commutative ring theory and representation Theory
  • Homological Algebra and Derived Functors.

    Schedule of Lectures

    Class Topic Suggested Reading Exercises
    Jan 16 Introduction. Topological Groups
    Jan 20 Lie groups: definitions
    Jan 23 Lie groups: exponential map, 1-parameter subgroup, first Lie theorem
    Jan 26 Snow day
    Jan 30 Lie groups: Ad and ad, ad ane Lie Bracket; Cartan's theorem on closed subgroups Exercises 1