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Structure theory and representation of Lie algebras

Bachelor and Master Seminar Summersemester 2016


[ Program | References | Dates | Links ]

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 pre-knowledge 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:

  1. Definition of simple, semisimple and abelian Lie algebras
  2. Representation of Lie algebras
  3. Complexification of Lie algebras
  4. Semisimple Lie algebra and Cartan decomposition
  5. Structure theory
  6. Iwasawa decomposition
  7. Representation of complex semisimple Lie algebras
  8. Hermitian symmetric spaces
  9. Harish-Chandra realization

References

The suggested references are:

  1. Hall, B.C.: Lie Groups, Lie Algebras, and Representations. Band 222 in Graduate Texts in Mathematics Springer-Verlag, 2003.
  2. Varadarajan, V: Lie groups, Lie algebras and their representations. Springer-Verlag, 1974.
  3. Knapp, A.W.: Representation theory of Semisimple Groups. Princeton University Press, 1986.
  4. 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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