Twisted group rings of strongly unbounded representation type

• Autorzy: Leonid F. Barannyk , Dariusz Klein
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 16G30: Representations of orders, lattices, algebras over commutative rings
• 20C20: Modular representations and characters
• 20C25: Projective representations and multipliers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 100
• Numer: 2
• Strony: 265-287

Daty

wydano

2004

Twórcy

autor

Leonid F. Barannyk

• Institute of Mathematics, Pedagogical University of Słupsk, Arciszewskiego 22b, 76-200 Słupsk, Poland

autor

Dariusz Klein

• Institute of Mathematics, Pedagogical University of Słupsk, Arciszewskiego 22b, 76-200 Słupsk, Poland

Identyfikatory

DOI

10.4064/cm100-2-8