The periodicity conjecture for blocks of group algebras
Volume 138 / 2015
Colloquium Mathematicum 138 (2015), 283-294
MSC: Primary 16D50, 16E30, 20C20; Secondary 16G60, 16G70, 20C05.
DOI: 10.4064/cm138-2-12
Abstract
We describe the representation-infinite blocks $B$ of the group algebras $K G$ 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.
