• Course begins: October 9th, 2014.
  • Course time: 10-12 Thursday and Friday
  • Course location: M006
  • Exercise session: 14:30-16:00 Fridays (first session October 17th)
  • Exercise session location: M006
  • Office hours by appointment in M206
  • There will be oral final exams on February 4th (30 minutes each). To partipate one should regularly attend the lectures.

This will be a first course on Lie algebras. The only prerequisite will be some experience with (linear) algebra.

Although Lie algebras are fundamentally simple objects, they are central to several areas of physics and mathematics. A Lie algebra is vector space with a bilinear skew symmetric form satisfying the so called Jacobi identity. The prototypical example of such an algebra is the space of n by n matrices with the commutator bracket.

During this course we will analyze the structure of Lie algebras and their representations, that is maps of Lie algebras into the prototypical example above. The study of simple Lie algebras and their representations is tied to certain combinatorial data: Coxeter groups and diagrams. We will explore this connection.