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Finite groups of OTP projective representation type

Leonid F. Barannyk — 2012

Colloquium Mathematicae

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...

Finite-dimensional twisted group algebras of semi-wild representation type

Leonid F. Barannyk — 2010

Colloquium Mathematicae

Let G be a finite group, K a field of characteristic p > 0, and K λ G the twisted group algebra of G over K with a 2-cocycle λ ∈ Z²(G,K*). We give necessary and sufficient conditions for K λ G to be of semi-wild representation type in the sense of Drozd. We also introduce the concept of projective K-representation type for a finite group (tame, semi-wild, purely semi-wild) and we exhibit finite groups of each type.

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

Leonid F. BarannykDariusz Klein — 2012

Colloquium Mathematicae

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...

Twisted group rings of strongly unbounded representation type

Leonid F. BarannykDariusz Klein — 2004

Colloquium Mathematicae

Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and S λ G a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by I n d m ( S λ G ) the set of isomorphism classes of indecomposable S λ G -modules of S-rank m. We exhibit rings S λ G for which there exists a function f λ : such that f λ ( n ) n and I n d f λ ( n ) ( S λ G ) is an infinite set for every natural n > 1. In special cases f λ ( ) contains every natural number m >...

On twisted group algebras of OTP representation type

Leonid F. BarannykDariusz Klein — 2012

Colloquium Mathematicae

Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and G = G p × B is 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*). We give necessary and sufficient conditions for S λ G to be of OTP representation type, in the sense 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...

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

Leonid F. BarannykDariusz Klein — 2016

Colloquium Mathematicae

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

On indecomposable projective representations of finite groups over fields of characteristic p > 0

Leonid F. BarannykKamila Sobolewska — 2003

Colloquium Mathematicae

Let G be a finite group, F a field of characteristic p with p||G|, and F λ G the twisted group algebra of the group G and the field F with a 2-cocycle λ ∈ Z²(G,F*). We give necessary and sufficient conditions for F λ G to be of finite representation type. We also introduce the concept of projective F-representation type for the group G (finite, infinite, mixed) and we exhibit finite groups of each type.

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