The periodicity conjecture for blocks of group algebras

• Autorzy: Karin Erdmann , Andrzej Skowroński
• Języki publikacji: EN

Abstrakty

EN

We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.

Kategorie tematyczne

• 16D50: Injective modules, self-injective rings
• 16G60: Representation type (finite, tame, wild, etc.)
• 20C20: Modular representations and characters
• 16E30: Homological functors on modules (Tor, Ext, etc.)
• 20C05: Group rings of finite groups and their modules
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 2
• Strony: 283-294

Daty

wydano

2015

Twórcy

autor

Karin Erdmann

• Mathematical Institute, University of Oxford, ROQ, Oxford OX2 6GG, United Kingdom

autor

Andrzej Skowroński

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm138-2-12