Universität Wien

250108 VO Algebraic Groups II (2017W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

The lecture course starts in the second (!) week of October, i.e. the first lecture is on
Monday, 9th of October !

  • Monday 02.10. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.10. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.10. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.10. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.10. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 06.11. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.11. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.11. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.11. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.12. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.12. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.01. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.01. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.01. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.01. 10:45 - 12:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The lecture course is a continuation of the lecture course "Algebraic groups" from the summer term. Basic knowledge of algebraic groups therefore will be assumed. Topics of the lecture course will be:

I.) Completion of the basics of the general theory of (affine) algebraic groups

1.) Lie algebra of an algebraic groups: adjoint representation; separable morphisms; semi linear automorphisms

2.) Construction of quotients of algebraic groups.

II.) Following this we want to look closer at the class of reductive algebraic groups which is important in number theory, geometry, representation theory. (An example of a reductive algebraic group is the algebraic group $GL_n$.) Here, the study of so called parabolic subgroups is central. A parabolic subgroup $P$ in an algebraic groups $G$ is a maximal solvable algebraic subgroup; these subgroups have a nice structure as do their quotients $G/P$; hence, they are ideally suited to study the structure of reductive algebraic groups.

3.) Parabolic subgroups

Finally, if time permits we want to look at the applications of Parabolic subgroups to/ their connections with the structure theory of reductive algebraic groups.

4.) Root systems of reductive algebraic groups

Assessment and permitted materials

Oral exam

Minimum requirements and assessment criteria

To pass the oral exam

Examination topics

Contents of the lecture course

Reading list

Borel: Linear Algebraic groups
Humphreys: Linear Algebraic groups
Springer: Linear Algebraic groups

Association in the course directory

MALV

Last modified: Mo 07.09.2020 15:40