Universität Wien

250105 VO Cohomology of groups and algebras (2018W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.10. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.10. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.10. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 11.10. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.10. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.10. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.10. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.10. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 29.10. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 05.11. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 08.11. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.11. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 15.11. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.11. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 22.11. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.11. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 29.11. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.12. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 06.12. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.12. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 13.12. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.01. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.01. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.01. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.01. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.01. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.01. 15:00 - 15:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.01. 15:00 - 16:30 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.01. 15:00 - 15:45 Hörsaal 13 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. Finally, Lie algebra cohomology is studied in detail.

Assessment and permitted materials

Written exam after the end of the lecture

Minimum requirements and assessment criteria

Prerequisites are Group Theory, Lie algebras and Abstract Algebra

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 07.09.2020 15:40