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# Lie Groups and Algebras

## Module MA5058

This Module is offered by TUM Department of Mathematics.

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 WS 2011/2 (current)

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 2011/2SS 2011

### Basic Information

MA5058 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from SS 2012 to SS 2012.

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

#### Learning and Teaching Methods

lecture, assignments

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)

### 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.

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