On indecomposable projective representations of finite groups over fields of characteristic $p>0$
Volume 98 / 2003
Colloquium Mathematicum 98 (2003), 171-187
MSC: 20C20, 20C25, 16S35.
DOI: 10.4064/cm98-2-4
Abstract
Let $G$ be a finite group, $F$ a field of characteristic $p$ with $p\mathchoice {\, |\, }{\, |\, }{|}{|}| G|$, and $F^{\lambda }G$ the twisted group algebra of the group $G$ and the field $F$ with a $2$-cocycle $\lambda \in Z^{2}( G,F^{\ast }) $. We give necessary and sufficient conditions for $F^{\lambda }G$ to be of finite representation type. We also introduce the concept of projective $F$-representation type for the group $G$ (finite, infinite, mixed) and we exhibit finite groups of each type.
