- Linear algebraic groups,
- Classical groups,
- Nilpotent and solvable groups,
- Borel subgroups,
- Root systems,
- Classification theorem,
- Structure of semisimple groups.
Algebraic Groups (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-43-20-M-7||Algebraic Groups||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|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.
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.
- 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.
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-40-11-M-4] Commutative Algebra (M, 9.0 LP)
- [MAT-12-11-K-2] Algebraic Structures (2V+2U, 5.5 LP)
- [MAT-12-22-K-3] Introduction to Algebra (2V+1U, 4.5 LP)
Requirements for attendance (formal)