250101 VO Selected topics in algebra (2006W)
Selected topics in algebra
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Details
Language: German
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Tuesday 10.10. 15:00 - 17:00 Seminarraum
- Friday 13.10. 13:00 - 15:00 Seminarraum
- Tuesday 17.10. 15:00 - 17:00 Seminarraum
- Friday 20.10. 13:00 - 15:00 Seminarraum
- Tuesday 24.10. 15:00 - 17:00 Seminarraum
- Friday 27.10. 13:00 - 15:00 Seminarraum
- Tuesday 31.10. 15:00 - 17:00 Seminarraum
- Friday 03.11. 13:00 - 15:00 Seminarraum
- Tuesday 07.11. 15:00 - 17:00 Seminarraum
- Friday 10.11. 13:00 - 15:00 Seminarraum
- Tuesday 14.11. 15:00 - 17:00 Seminarraum
- Friday 17.11. 13:00 - 15:00 Seminarraum
- Tuesday 21.11. 15:00 - 17:00 Seminarraum
- Friday 24.11. 13:00 - 15:00 Seminarraum
- Tuesday 28.11. 15:00 - 17:00 Seminarraum
- Friday 01.12. 13:00 - 15:00 Seminarraum
- Tuesday 05.12. 15:00 - 17:00 Seminarraum
- Tuesday 12.12. 15:00 - 17:00 Seminarraum
- Friday 15.12. 13:00 - 15:00 Seminarraum
- Tuesday 09.01. 15:00 - 17:00 Seminarraum
- Friday 12.01. 13:00 - 15:00 Seminarraum
- Tuesday 16.01. 15:00 - 17:00 Seminarraum
- Friday 19.01. 13:00 - 15:00 Seminarraum
- Tuesday 23.01. 15:00 - 17:00 Seminarraum
- Friday 26.01. 13:00 - 15:00 Seminarraum
- Tuesday 30.01. 15:00 - 17:00 Seminarraum
Information
Aims, contents and method of the course
We discuss the cohomology of Lie algebras with general coefficients. First we introduce the cohomology via the explicit formula for the coboundary operator. We discuss the cohomology groups in low degrees and the classical interpretation of these cohomology groups, i.e., the interpretation via extension theory and crossed modules. Thereafter we introduce cohomology on a very general level via derived functors and categories. We will give some more details on abelian categories. Finally we discuss several applications of Lie algebra cohomology in the context of differential geometry and number theory. Furthermore we study the total cohomology and the relative Lie algebra cohomology.
Assessment and permitted materials
Minimum requirements and assessment criteria
Examination topics
Reading list
1.) Jacobson, Nathan: Lie algebras. 1962
2.) Weibel, C.A.: An introduction to homological algebra. 1997
3.) Hilton, O.S., Stammbach, U.: A course in homological algebra. 1997
4.) Cartan, E., Eilenberg, S.: Homological algebra. 1956
5.) Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. 1948
6.) Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
7.) Knapp, Anthony W.: Lie groups, Lie algebras, and cohomology. 1988
8.) Hilgert, Joachim; Neeb, Karl-Hermann: Lie-Gruppen und Lie-Algebren. 1991
2.) Weibel, C.A.: An introduction to homological algebra. 1997
3.) Hilton, O.S., Stammbach, U.: A course in homological algebra. 1997
4.) Cartan, E., Eilenberg, S.: Homological algebra. 1956
5.) Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. 1948
6.) Bourbaki, Nicolas: Lie groups and Lie algebras. 1975
7.) Knapp, Anthony W.: Lie groups, Lie algebras, and cohomology. 1988
8.) Hilgert, Joachim; Neeb, Karl-Hermann: Lie-Gruppen und Lie-Algebren. 1991
Association in the course directory
Last modified: Mo 07.09.2020 15:40