Universität Wien
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250041 VO Cohomology of Groups and Algebras (2022W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
ON-SITE

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 03.10. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.10. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.10. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.10. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 24.10. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.10. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.11. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.11. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.11. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.11. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.11. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.12. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 07.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.12. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.12. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.01. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.01. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 23.01. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.01. 13:15 - 14:45 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 30.01. 13:15 - 14:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Group homology and cohomology has its origin in topology. With the rise of
the algebraic methods the homology and cohomology of several algebraic systems
was defined and explored.
We start the lecture by giving an elementary definition of group cohomology,
along with group extensions and factor systems. We give interpretations of
the n-th cohomology group for small n.
Then we will study the functorial definition of cohomology. In the last part we will treat
Lie algebra homology and cohomology, along with some applications.

Assessment and permitted materials

Written exam after the end of the lecture.

Minimum requirements and assessment criteria

Passing the exam (at least half of the points).

Examination topics

Split exact sequences and group extensions
Factor systems and equivalent group extensions
G-modules and low-degree cohomology groups
Functors, resolutions and cohomology
Lie algebras and Lie algebra cohomology

Reading list

[WEI] Weibel, C. A., An introduction to homological algebra. Cambridge University Press 1997.
[WES] Weiss, E., Cohomology of groups. Pure and Applied Mathematics, 34 Academic Press 1969.
[CAE] Cartan, E., Eilenberg, S.: Homological algebra. 1956
[CHE] Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. 1948
[KNA] Knapp, A. W.: Lie groups, Lie algebras, and cohomology. 1988

Association in the course directory

MALV

Last modified: Mo 30.01.2023 16:59