On twisted group algebras of OTP representation type

Leonid F. Barannyk¹ ; Dariusz Klein¹

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 $p$, $S^{\ast }$ 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 $p^{\prime }$-group. Denote by $S^{\lambda }G$ the twisted group algebra of $G$ over $S$ with a $2$-cocycle $\lambda \in Z^2(G,S^{\ast })$. 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 $V\mathrm{\#}W$ of an indecomposable $S^{\lambda }{G}_p$-module $V$ and an irreducible $S^{\lambda }B$-module $W$.

Détail

DOI : 10.4064/cm127-2-5

Mots-clés : 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