Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

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

Abstrakty

EN

Let S be a commutative complete discrete valuation domain of positive characteristic p, S* the unit group of S, Ω a subgroup of S* and $G = G_{p} × B$ a finite group, where $G_{p}$ is a p-group and B is a p'-group. Denote by $S^{λ}G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). For Ω satisfying a specific condition, we give necessary and sufficient conditions for G to be of OTP projective (S,Ω)-representation type, in the sense that there exists a cocycle λ ∈ Z²(G,Ω) such that every indecomposable $S^{λ}G$-module is isomorphic to the outer tensor product V # W of an indecomposable $S^{λ}G_{p}$-module V and an irreducible $S^{λ}B$-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: 2012
• Tom: 129
• Numer: 2
• Strony: 173-187

Daty

wydano

2012

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/cm129-2-2