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

• Autorzy: Leonid F. Barannyk , Dariusz Klein
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16G60: Representation type (finite, tame, wild, etc.)
• 20C20: Modular representations and characters
• 20C25: Projective representations and multipliers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 143
• Numer: 2
• Strony: 209-235

Daty

wydano

2016

Twórcy

autor

Leonid F. Barannyk

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

autor

Dariusz Klein

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

Identyfikatory

DOI

10.4064/cm6700-1-2016