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1
Content available remote

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

100%
Barannyk L.
Colloquium Mathematicum
|
2010
|
tom 120
|
nr 2
277-298
EN
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.
2
Content available remote

On faithful projective representations of finite abelian p-groups over a field of characteristic p

100%
Barannyk L.
Colloquium Mathematicum
|
2008
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tom 111
|
nr 1
135-147
EN
Let G be a noncyclic abelian p-group and K be an infinite field of finite characteristic p. For every 2-cocycle λ ∈ Z²(G,K*) such that the twisted group algebra $K^{λ}G$ is of infinite representation type, we find natural numbers d for which G has infinitely many faithful absolutely indecomposable λ-representations over K of dimension d.
3
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Finite groups of OTP projective representation type

100%
Barannyk L.
Colloquium Mathematicum
|
2012
|
tom 126
|
nr 1
35-51
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.
4
Content available remote

On modular projective representations of finite nilpotent groups

64%
Barannyk L., Sobolewska K.
Colloquium Mathematicum
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2001
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tom 87
|
nr 2
181-193
EN
Our aim is to determine necessary and sufficient conditions for a finite nilpotent group to have a faithful irreducible projective representation over a field of characteristic p ≥ 0.
5
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Finite groups of OTP projective representation type over a complete discrete valuation domain of positive characteristic

64%
Barannyk L., Klein D.
Colloquium Mathematicum
|
2012
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tom 129
|
nr 2
173-187
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.
6
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On indecomposable projective representations of finite groups over fields of characteristic p > 0

64%
Barannyk L., Sobolewska K.
Colloquium Mathematicum
|
2003
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tom 98
|
nr 2
171-187
EN
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.
7
Content available remote

Twisted group rings of strongly unbounded representation type

64%
Barannyk L., Klein D.
Colloquium Mathematicum
|
2004
|
tom 100
|
nr 2
265-287
EN
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 $Ind_{m}(S^{λ}G)$ 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}: ℕ → ℕ $ such that $f_{λ}(n) ≥ n$ and $Ind_{f_{λ}(n)}(S^{λ}G)$ is an infinite set for every natural n > 1. In special cases $f_{λ}(ℕ)$ contains every natural number m > 1 such that $Ind_{m}(S^{λ}G)$ is an infinite set. We also introduce the concept of projective (S,W)-representation type for the group G and we single out finite groups of every type.
8
Content available remote

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

64%
Barannyk L., Klein D.
Colloquium Mathematicum
|
2016
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tom 143
|
nr 2
209-235
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.
9
Content available remote

On twisted group algebras of OTP representation type

64%
Barannyk L., Klein D.
Colloquium Mathematicum
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2012
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tom 127
|
nr 2
213-232
EN
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 W.
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