Representations of Compact Groups
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2018
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|SS 2019||SS 2018||SS 2015|
MA5054 is a semester module in English language at Master’s level which is offered irregular.
This module description is valid from SS 2018 to SS 2018.
|Total workload||Contact hours||Credits (ECTS)|
|180 h||45 h||6 CP|
Content, Learning Outcome and Preconditions
MA1002 - Analysis 2
MA1101 - Linear Algebra and Discrete Structures1
MA1002 - Linear Algebra and Discrete Structures 2
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|VO||2||Representations of Compact Groups||König, R.|
|UE||1||Representations of Compact Groups (Exercise Session)||König, R.|
Learning and Teaching Methods
This module consists of lectures together with accompanying practice sessions. The lectures will convey relevant concepts, mathematical results and proof methods along with concrete examples by means of board work and through discussion with the students. This is intended to motivate students to study the literature and approach problems independently. Practice sessions will be offered which complement the theoretical material developed in the lectures. Exercise sheets and solutions will be provided, which will help students to deepen their understanding, and independently assess their progress. The practice sessions will be guided initially, but will proceed throughout the term to more independent work by students individually as well as in small groups.
Description of exams and course work
The exam will assess the ability to give precise definitions, prove selected theorems involving algebraic, differential geometric and analytical arguments, and apply results and techniques to analyze, classify and construct various algebraic objects appearing in the study of Lie groups and algebras. This includes, in particular, the problem of decomposing representations into irreducibles. With suitably chosen examples, the ability to transfer results and techniques to the analysis of related problems involving representation-theoretic concepts will be tested.
The exam may be repeated at the end of the semester.