In this seminar, we will learn the basic theory of algebraic groups over any algebraic closed fields. More precisely, we shall concentrate on linear algebraic groups, which is a closed subvariety of the general linear group GL(n).

Linear algebraic groups play an important role in many areas of mathematics especially in geometry and representation theory. We shall deal with the following notations:

• the Lie algebra of an algebraic group;
• quotient of an algebraic group by a closed subgroup;
• tori, solvable groups and Borel subgroups;
• structure of reductive groups;
• classification of semisimple algebraic groups;
• representations of semisimple algebraic groups.

References:

• J.E. Humphreys: Linear algebraic groups,Modern Birkhauser Classics
• A. Borel: Linear algebraic groups, GTM 126
• T.A. Springer: Linear algebraic groups, GTM 21

• Organisational meeting/distribution of topics: On 27.07.2017 at 16:00 in M223 or by email:
  yigeng.zhao@ur.de
• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk