250041 VO Cohomology of Groups and Algebras (2022W)
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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
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
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
[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
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.