Lie Groups and Algebras
Module MA5058
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 2011
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 | |
|---|---|
| WS 2011/2 | SS 2011 |
Basic Information
MA5058 is a semester module in German or English language at Master’s level which is offered irregular.
This module description is valid from SS 2012 to SS 2012.
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 30 h | 5 CP |
Content, Learning Outcome and Preconditions
Content
Linear Lie groups. Lie algebras. Baker-Campbell-Hausdorff formula. Lie subgrous and Lie subalgebras. Solvable and nilpotent Lie algebras. Root systems and Weyl groups.
Learning Outcome
At the end of the module, students are able to understand the algebraic and geometric features of Lie groups and algebras, and apply the concepts to analytical and topological settings.
Preconditions
MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Lie Groups and Algebras | Massopust, P. | ||
| UE | 1 | Lie Groups and Algebras (Exercise session) | Massopust, P. |
Learning and Teaching Methods
lecture, assignments
Media
blackboard
Literature
J. Hilgert u. K.-H. Neeb, Lie-Gruppen und Lie-Algebren, Vieweg Verlag, 1991. (begleitend),
M. Hausner u. J. Schwartz, Lie Groups; Lie Algebras, Gordon & Breach 1968. (begleitend),
A. Sagle u. R. Walde, Introduction to Lie Groups and Lie Algebras, Academic Press, 1973. (begleitend),
N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4 - 6, Springer Verlag, 2002. (weiterführend),
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, AMS Graduate Texts in Mathematics, Vol. 34, 1978. (weiterführend)
M. Hausner u. J. Schwartz, Lie Groups; Lie Algebras, Gordon & Breach 1968. (begleitend),
A. Sagle u. R. Walde, Introduction to Lie Groups and Lie Algebras, Academic Press, 1973. (begleitend),
N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4 - 6, Springer Verlag, 2002. (weiterführend),
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, AMS Graduate Texts in Mathematics, Vol. 34, 1978. (weiterführend)
Module Exam
Description of exams and course work
The module examination is based on a 30-minute oral exam. Students are able to understand the algebraic and geometric features of Lie groups and algebras, and apply the concepts to analytical and topological settings.
Exam Repetition
The exam may be repeated at the end of the semester.