241014 Representations of Algebras II (V) (WiSe 2025/2026)

Contents, comment

I want to cover a number of key topics in the representation theory of finite-dimensional associative algebras:

Correspondences given by faithfully balanced modules, and applications to Auslander algebras and homological conjectures. (Originally planned for the previous semester, but carried over, since there was not enough time.)

Tilting and tau-tilting theory, including equivalences of derived categories.

Geometric methods for studying representations of algebras, including relevant facts about varieties and schemes without proofs. (There will be less time for this than originally planned.)

If time, possibly preprojective algebras and Kleinian singularities.

Requirements for participation, required level

Students are expected to have some familiarity with rings and modules, and topics such as categories, projective and injective modules, and Ext groups. I will freely use ideas and results from the previous course in the sequence "Representations of Algebras".

External comments page

https://www.math.uni-bielefeld.de/~wcrawley/2526RAII/

Teaching staff

Dates ( Calendar view )

Frequency Weekday Time Format / Place Period  
weekly Mo 10-12 X-E0-212 13.10.2025-06.02.2026
weekly Do 14-16 B2-212 13.10.2025-06.02.2026

Subject assignments

Module Course Requirements  
24-M-M2 Mathematics 2 Mathematics 2 - Variante 1 Student information
24-M-P1 Profilierung 1 Profilierungsvorlesung (mit Übung) - Typ 1 Student information
24-M-P1a Profilierung 1 Teil A Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-P1b Profilierung 1 Teil B Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-P2 Profilierung 2 Profilierungsvorlesung (mit Übungen) - Typ 1 Student information
24-M-PWM Profilierung Wirtschaftsmathematik Profilierungsvorlesung (mit Übung) - Typ 1 Student information
- Graded examination Student information
24-M-S2-AL Spezialisierung 2 - Algebra Masterkurs 1 Algebra - Variante 1 Student information
24-M-V2-AL Vertiefung 2 - Algebra Masterkurs 1 Algebra - Variante 1 Study requirement
Student information
- Graded examination Student information

The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.

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Address:
WS2025_241014@ekvv.uni-bielefeld.de
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Last update basic details/teaching staff:
Wednesday, June 25, 2025 
Last update times:
Tuesday, August 19, 2025 
Last update rooms:
Tuesday, August 19, 2025 
Type(s) / SWS (hours per week per semester)
lecture (V) / 4
Language
This lecture is taught in english
Department
Faculty of Mathematics
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567984397