Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-43-13-M-7

Lie Algebras (M, 9.0 LP, AUSL)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-13-M-7 Lie Algebras 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 [AUSL] Phase-out period

Notice

The module was replaced by [MAT-43-27-M-7] Lie Algebras and their Representation Theory.

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-43-13-K-7
Lie Algebras
P 56 h 214 h - - PL1 9.0 irreg.
  • About [MAT-43-13-K-7]: Title: "Lie Algebras"; Presence-Time: 56 h; Self-Study: 214 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination number: 86268 ("Lie Algebras")

Evaluation of grades

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


Contents

Part 1:
  • finite reflection groups, root systems,
  • classification of the semisimple complex Lie algebras.

Part 2:

  • resolvable and nilpotent Lie algebras,
  • representation theory of semisimple complex Lie algebras.

Competencies / intended learning achievements

Upon successful completion of this module, the students are familiar with and understand the basic methods and assumptions of the theory of Lie algebras. They have become acquainted with significant examples and are able to examine them by using scientific methods. 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 are able to reproduce and explain them. In particular, they can critically assess what conditions are necessary for the validity of the statements.

By completing exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture.

Literature

  • J. E. Humphreys: Introduction to Lie Algebras and Representation Theory,
  • K. Erdmann: Introduction to Lie Algebras.

References to Module / Module Number [MAT-43-13-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.)