Module Handbook

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Module MAT-43-27-M-7

Lie Algebras and their Representation Theory (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-43-27-M-7 Lie Algebras and their Representation Theory 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
+ further Lecturers of the department Mathematics
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

Notice

This module replaces the previous module [MAT-43-13-M-7] Lie Algebras.

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-43-27-K-7
Lie Algebras and their Representation Theory
P 84 h 186 h - - PL1 9.0 irreg.
  • About [MAT-43-27-K-7]: Title: "Lie Algebras and their Representation Theory"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86269 ("Lie Algebras and their Representation Theory")

Evaluation of grades

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


Contents

  • general concept of Lie algebras and their relation to Lie groups
  • classification of the semi-simple (complex) Lie algebras
  • fundamentals of the representation theory of semisimple Lie algebras
  • combinatorial structures of Lie theory: root systems, Weyl groups, Dynkin diagrams.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand the fundamental methods and statements of the theory of Lie algebras as well as their representation theory and they know the relation of Lie algebras to Lie groups. They have learned important examples of Lie algebras and are able to investigate them by using scientific methods. They are able to name the essential statements of the lecture and to classify and explain the presented connections. They understand the proofs presented in the lecture and are able to reproduce and explain them. In particular, they can outline the conditions and assumptions that are necessary for the validity of the statements.

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

Literature

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

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Knowledge from the module [MAT-40-25-M-4] is desirable and helpful, but is not mandatory.

Modules:

Courses

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-43-27-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.)