This is an introduction to linear algebraic groups, a subject on the interface of group theory, linear algebra and algebraic geometry.
We cover the basic theory of linear algebraic groups over algebraically closed fields, including Jordan form and the Lie-Kolchin theorem, homogeneous spaces and quotient constructions, Borel subgroups, maximal tori and root systems. The necessary background in algebraic geometry will be developed from scratch along the way.
- regular homework, and presentation or final
Topics in Algebra