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.
- 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
- 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.