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401-3207-58L 10 Credits BSC , DR , MSC D-USYS , D-BAUG , D-MAVT , D-INFK , D-MTEC , D-MATH , D-PHYS , D-BIOL , D-ERDW , D-GESS , D-ITET , D-ARCH , D-CHAB

Homological Algebra and Modular Representation Theory

Homologische Algebra und modulare Darstellungstheorie

Lecturers & Examiners: Prof. Dr. Karin Ursula Baur
VVZ CR n/a

Last Updated: 2026-02-05 15:25:11

Abstract

Categories and functors.Free, projective, injective, flat modules. Snake Lemma.Chain complexes, (co-)homology, homotopy, projective resolutions.Derived functors; Ext-groups.Blocks of an algebra.Representations of finite groups in positive characteristic.Triangulated categories.

Objective

Categories, functors, tensor products. Sums, products, exact sequences. Adjoints, Pushouts, Pullbacks, Limits. Free, projective, injective, flat modules. Homology, Snake Lemma, chain complexes, homotopy. Derived functors. Ext und SES's: Ext^1, Yoneda product, quiver of an algebra. Some homological dimensions. Cohomology of finite groups, projective indecomposable modules. Representations of finite groups in positive characteristic.

General Information

Language
German
Levels
BSC , DR , MSC

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Homologische Algebra und modulare Darstellungstheorie
  • Tue 10:15-12:00 (HG D 5.2)
  • Thu 13:15-15:00 (HG G 3)
4 h weekly
exercise Homologische Algebra und modulare Darstellungstheorie
  • Thu 11:15-12:00 (HG G 26.3)
  • Fri 15:15-16:00 (HG G 26.1)
1 h weekly

Offered In