Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-43-25-M-7

Algebraic Groups II (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-25-M-7 Algebraic Groups II 4.5 CP (135 h)

Basedata

CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers
Area of study [MAT-AGCA] Algebra, Geometry and Computer Algebra
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V MAT-43-25-K-7
Algebraic Groups II
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-43-25-K-7]: Title: "Algebraic Groups II"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: irregular (by arrangement)
  • Examination number: 86125 ("Algebraic Groups II")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • BN Pairs,
  • parabolic subgroups,
  • subgroups of maximum rank,
  • rational representations.

Competencies / intended learning achievements

Upon successful completion of this module, the students are familiarized with a class of important groups and algebraic varieties, which play a significant role in many areas of mathematics. They have learnt how the methods of group theory and algebraic geometry can complement eachother and lead to deeper understanding. They are able to name the essential propositions of the lecture as well as to classify and to explain the connections. They understand the proofs presented in the lecture and will be able to comprehend and explain them.

Literature

  • G. Malle, D. Testermann: Linear Algebraic Groups and Finite Groups of Lie Type,
  • J.E Humphreys: Linear Algebraic Groups,
  • T. Springer: Linear Algebraic Groups.

Requirements for attendance (informal)

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-43-25-M-7]

Module-Pool Name
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)