On twisted group algebras of OTP representation type over the ring of p-adic integers

Leonid F. Barannyk ; Dariusz Klein

Colloquium Mathematicae, Tome 144 (2016), p. 209-235 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $ℤ̂_{p}$ be the ring of p-adic integers, $U(ℤ̂_{p})$ the unit group of $ℤ̂_{p}$ and $G = G_{p} × B$ a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $ℤ̂_{p}^{λ}G$ the twisted group algebra of G over $ℤ̂_{p}$ with a 2-cocycle $λ ∈ Z²(G,U(ℤ̂_{p}))$. We give necessary and sufficient conditions for $ℤ̂_{p}^{λ}G$ to be of OTP representation type, in the sense that every indecomposable $ℤ̂_{p}^{λ}G$-module is isomorphic to the outer tensor product V W of an indecomposable $ℤ̂_{p}^{λ}G_{p}$-module V and an irreducible $ℤ̂_{p}^{λ}B$-module W.

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Publié le : 2016-01-01

Zbl 06574983

EUDML-ID : urn:eudml:doc:283543