Structure theory and representation of Lie algebras
Bachelor and Master Seminar Summersemester 2016
Program
This seminar contains different aspects of structure and representation theory
of Lie algebras. They can be treated at different levels, depending on the background
of the student. Bachelor students can approach the basic structure theory, which does not
need any preknowledge in differential geometry, and its application in representation theory.
Master student can study more advanced representation theory, which needs some basic tools
of holomorphic functions and differential geometry.
Topics:
 Definition of simple, semisimple and abelian Lie algebras
 Representation of Lie algebras
 Complexification of Lie algebras
 Semisimple Lie algebra and Cartan decomposition
 Structure theory
 Iwasawa decomposition
 Representation of complex semisimple Lie algebras
 Hermitian symmetric spaces
 HarishChandra realization
References
The suggested references are:

Hall, B.C.:
Lie Groups, Lie Algebras, and Representations.
Band 222
in Graduate Texts in Mathematics
SpringerVerlag,
2003.

Varadarajan, V:
Lie groups, Lie algebras and their representations.
SpringerVerlag,
1974.

Knapp, A.W.:
Representation theory of Semisimple Groups.
Princeton University Press,
1986.

Helgason, S.:
Differential geometry and Symmetric spaces.
Academy Press,
1962.
Dates
The first meeting will take place on Monday 11th April at 14:00 in
my office (31.00.002).
Links
The seminar will appear soon on Wuecampus...
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