## MAT 1110: Linear Algebraic Groups, Winter 2017

**Instructor:** Florian Herzig;
my last name at math dot toronto dot edu

**Office Hours:** by appointment, at BA 6186

**Lectures:** Tuesdays 3-5pm, Fridays 4-5pm at HU 1018

### Syllabus

This course will be an introduction to the theory of linear algebraic groups over an algebraically closed field. Algebraic
groups are algebraic varieties equipped with a group structure such that the group operations are given by maps of algebraic
varieties. An algebraic group is called linear if it can be embedded as a closed subgroup of a general linear group. This
includes, for example, special linear, symplectic, and orthogonal groups. The subject has many parallels with the classical
theory of (compact) Lie groups and Lie algebras.

### Outline:

- varieties, affine algebraic groups, quotients
- Lie algebras
- diagonalisable, unipotent, and solvable algebraic groups - Borel subgroups, parabolic subgroups
- Weyl group, Bruhat decomposition
- structure theory of reductive groups

### Prerequisites:

- Basic algebraic geometry (affine and projective varieties over an algebraically closed field)
- Graduate algebra

### References:

- Course notes (please send me typos!)
- Springer, Linear algebraic groups, Birkhauser
- Patrick Polo's course notes
- Borel, Linear algebraic groups, Springer GTM
- Humphreys, Linear algebraic groups, Springer GTM

### Homework