On twisted group algebras of OTP representation type
Volume 127 / 2012
Colloquium Mathematicum 127 (2012), 213-232
MSC: Primary 16G60; Secondary 20C20, 20C25.
DOI: 10.4064/cm127-2-5
Abstract
Assume that $S$ is a commutative complete discrete valuation domain of characteristic $p$, $S^*$ is the unit group of $S$ and $G=G_p\times B$ is a finite group, where $G_p$ is a $p$-group and $B$ is a $p'$-group. Denote by $S^\lambda G$ the twisted group algebra of $G$ over $S$ with a $2$-cocycle $\lambda \in Z^2(G,S^*)$. We give necessary and sufficient conditions for $S^\lambda G$ to be of OTP representation type, in the sense that every indecomposable $S^\lambda G$-module is isomorphic to the outer tensor product $V\mathbin {\#}W$ of an indecomposable $S^\lambda G_p$-module $V$ and an irreducible $S^\lambda B$-module $W$.
