Finite groups of OTP projective representation type

• Autorzy: Leonid F. Barannyk
• Języki publikacji: EN

Abstrakty

EN

Let K be a field of characteristic p > 0, K* the multiplicative group of K and $G = G_{p} × B$ a finite group, where $G_{p}$ is a p-group and B is a p'-group. Denote by $K^{λ}G$ a twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for G to be of OTP projective K-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,K*) such that every indecomposable $K^{λ}G$-module is isomorphic to the outer tensor product V # W of an indecomposable $K^{λ}G_{p}$-module V and a simple $K^{λ}B$-module W. We also exhibit finite groups $G = G_{p} × B$ such that, for any λ ∈ Z²(G,K*), every indecomposable $K^{λ}G$-module satisfies this condition.

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: 2012
• Tom: 126
• Numer: 1
• Strony: 35-51

Daty

wydano

2012

Twórcy

autor

Leonid F. Barannyk

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

Identyfikatory

DOI

10.4064/cm126-1-2