Finite groups of OTP projective representation type

Leonid F. Barannyk. "Finite groups of OTP projective representation type." Colloquium Mathematicae 126.1 (2012): 35-51. <http://eudml.org/doc/283789>.

@article{LeonidF2012,
abstract = {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.},
author = {Leonid F. Barannyk},
journal = {Colloquium Mathematicae},
keywords = {modular representations; outer tensor products; projective representations; representation types; twisted group algebras},
language = {eng},
number = {1},
pages = {35-51},
title = {Finite groups of OTP projective representation type},
url = {http://eudml.org/doc/283789},
volume = {126},
year = {2012},
}

TY - JOUR
AU - Leonid F. Barannyk
TI - Finite groups of OTP projective representation type
JO - Colloquium Mathematicae
PY - 2012
VL - 126
IS - 1
SP - 35
EP - 51
AB - 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.
LA - eng
KW - modular representations; outer tensor products; projective representations; representation types; twisted group algebras
UR - http://eudml.org/doc/283789
ER -