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Instructors: Prof. Dr. Ingo Runkel
Event type:
Lecture
Displayed in timetable as:
M-VAlg-V
Hours per week:
4
Language of instruction:
English
Min. | Max. participants:
- | -
Comments/contents:
The importance of Lie algebras derives from their relation to Lie
groups. A Lie group is a group and a manifold, such that the group
operations are smooth maps. They often arise as symmetry groups in
physics and mathematics. The group SO(n) of rotations in R^n is such an
example. Lie algebras, the topic of this course, in turn are
"linearisations" of Lie groups, or "infinitesimal symmetry
transformations". They consist of a vector space together with a
bilinear operation, the Lie bracket. Surprisingly, many of the
properties of Lie groups can derived from these linearisations. We will
study:
* definition and basic properties of Lie algebras,
* nilpotent and solvable Lie algebras,
* universal enveloping algebra and PBW-basis,
* semisimple Lie algebras: root systems, Dynkin diagrams,
classification, and
* highest weight representations.
This course is mainly aimed at Masters students in Mathematics and
Mathematical Physics.
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