On twisted group algebras of OTP representation type

Leonid F. Barannyk ¹   ; Dariusz Klein ¹

¹ Institute of Mathematics Pomeranian University of Słupsk Arciszewskiego 22d 76-200 Słupsk, Poland

Colloquium Mathematicum, Tome 127 (2012) no. 2, pp. 213-232

Résumé

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 $W$.

Détail

DOI : 10.4064/cm127-2-5

Keywords: assume commutative complete discrete valuation domain characteristic * unit group times finite group where p group p group denote lambda twisted group algebra cocycle lambda * necessary sufficient conditions lambda otp representation type sense every indecomposable lambda g module isomorphic outer tensor product mathbin indecomposable lambda p module irreducible lambda b module