Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-43-20-M-7

Algebraic Groups (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-20-M-7 Algebraic Groups 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 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.
4V MAT-43-20-K-7
Algebraic Groups
P 56 h 214 h - - PL1 9.0 irreg.
  • About [MAT-43-20-K-7]: Title: "Algebraic Groups"; Presence-Time: 56 h; Self-Study: 214 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86118 ("Algebraic Groups")

Evaluation of grades

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


Contents

  • Linear algebraic groups,
  • Classical groups,
  • Nilpotent and solvable groups,
  • Borel subgroups,
  • Root systems,
  • Classification theorem,
  • Structure of semisimple groups.

Competencies / intended learning achievements

Upon successful completion of this module, the students are familiarized with a large 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 each other and lead to a better 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.

Requirements for attendance (informal)

Knowledge from the course [MAT-40-12-K-7] is useful but not necessarily required.

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-43-20-M-7]

Module-Pool Name
[MAT-41-MPOOL-7] Specialisation Algebraic Geometry and Computer Algebra (M.Sc.)
[MAT-43-MPOOL-7] Specialisation Algebra and Number Theory (M.Sc.)
[MAT-RM-MPOOL-7] Pure Mathematics (Advanced Modules M.Sc.)