Semi-invariants and weights of group algebras of finite groups

Abstract

We study the semi-invariants and weights of a group algebra K[G] over a field K of characteristic zero. Specifically, we show that certain basic results which hold when G is a polycyclic-by-finite group with Delta(+) (G) = 1 need not hold in the case of group algebras of finite groups. This turns out to be a purely group theoretic question about the existence of class preserving automorphisms.