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Lecture Course on Algebra (Master)
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Birgit Richter, email: birgit.richter at
uni-hamburg.de
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| Plan: |
The aim of this course is to present the basics of homological
algebra. Methods from homological algebra are used in
many areas of pure mathematics. I will develop the
theoretical background (rings and modules, basics from
category theory) and then discuss resolutions and
derived functors. Our two main applications are
Hochschild homology (which is a homology theory for
associative algebras) and group homology. Homological
algebra is pretty useless unless you are able to
calculate things, so I'll also discuss spectral
sequences.
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| | If you plan to do a master thesis on a topic
related to this lecture course, then please contact me as early
as possible. |
| Literature: |
Here are lecture notes for this course.
Beware, these are probably full of typos and mistakes. Use at your own risk!
- Brown, Kenneth S. Cohomology of groups. Corrected reprint of the
1982 original. Graduate Texts in Mathematics, 87. Springer-Verlag,
New York, 1994. x+306 pp.
- Loday, Jean-Louis, Cyclic homology. Second edition. Grundlehren
der Mathematischen Wissenschaften 301. Springer-Verlag, Berlin,
1998. xx+513 pp.
- McCleary, John,
A user's guide to spectral sequences,
Second edition. Cambridge Studies in Advanced Mathematics,
58. Cambridge University Press, Cambridge, 2001. xvi+561 pp.
- Richter, Birgit, From Categories to Homotopy Theory, Cambridge Studies
in Advanced Mathematics 188, 2020. x+390 pp..
- Rotman, Joseph J. An introduction to homological algebra. Second
edition. Universitext. Springer, New York, 2009. xiv+709 pp.
- Weibel, Charles, An introduction to homological algebra. Cambridge
Studies in Advanced Mathematics, 38. Cambridge University Press,
Cambridge, 1994. xiv+450 pp.
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| Exam: |
The final exam for this course is an oral exam after the end of term. In
order to qualify for the exam, you have to present solutions to the
weekly exercises four times in the exercise class.
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| When?: |
The exercise class for this lecture is We 2:30-4pm via zoom. You find the login data in STiNE and moodle.
The videos for the lecture course are avaible via the moodle page of the course. You find the subscription key for moodle in STiNE.
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