Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk, and Dariusz Klein. "Twisted group rings of strongly unbounded representation type." Colloquium Mathematicae 100.2 (2004): 265-287. <http://eudml.org/doc/284144>.

@article{LeonidF2004,
abstract = {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.},
author = {Leonid F. Barannyk, Dariusz Klein},
journal = {Colloquium Mathematicae},
keywords = {twisted group rings; representation types; projective representations; modular representations},
language = {eng},
number = {2},
pages = {265-287},
title = {Twisted group rings of strongly unbounded representation type},
url = {http://eudml.org/doc/284144},
volume = {100},
year = {2004},
}

TY - JOUR
AU - Leonid F. Barannyk
AU - Dariusz Klein
TI - Twisted group rings of strongly unbounded representation type
JO - Colloquium Mathematicae
PY - 2004
VL - 100
IS - 2
SP - 265
EP - 287
AB - 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.
LA - eng
KW - twisted group rings; representation types; projective representations; modular representations
UR - http://eudml.org/doc/284144
ER -