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

Leonid F. Barannyk, and Dariusz Klein. "On twisted group algebras of OTP representation type over the ring of p-adic integers." Colloquium Mathematicae 143.2 (2016): 209-235. <http://eudml.org/doc/283543>.

@article{LeonidF2016,
abstract = {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.},
author = {Leonid F. Barannyk, Dariusz Klein},
journal = {Colloquium Mathematicae},
keywords = {outer tensor product; projective representation; representation type; twisted group algebra},
language = {eng},
number = {2},
pages = {209-235},
title = {On twisted group algebras of OTP representation type over the ring of p-adic integers},
url = {http://eudml.org/doc/283543},
volume = {143},
year = {2016},
}

TY - JOUR
AU - Leonid F. Barannyk
AU - Dariusz Klein
TI - On twisted group algebras of OTP representation type over the ring of p-adic integers
JO - Colloquium Mathematicae
PY - 2016
VL - 143
IS - 2
SP - 209
EP - 235
AB - 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.
LA - eng
KW - outer tensor product; projective representation; representation type; twisted group algebra
UR - http://eudml.org/doc/283543
ER -