Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk; Dariusz Klein

Colloquium Mathematicae, Tome 100 (2004), p. 265-287 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $I n d_{m} (S^{λ} G)$ 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 $f_{λ} : ℕ \to ℕ$ such that $f_{λ} (n) \geq n$ and $I n d_{f_{λ} (n)} (S^{λ} G)$ is an infinite set for every natural n > 1. In special cases $f_{λ} (ℕ)$ contains every natural number m > 1 such that $I n d_{m} (S^{λ} G)$ 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.

Publié le : 2004-01-01

Zbl 1069.16030

EUDML-ID : urn:eudml:doc:284144

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     author = {Leonid F. Barannyk and Dariusz Klein},
     title = {Twisted group rings of strongly unbounded representation type},
     journal = {Colloquium Mathematicae},
     volume = {100},
     year = {2004},
     pages = {265-287},
     zbl = {1069.16030},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-2-8}
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Leonid F. Barannyk; Dariusz Klein. Twisted group rings of strongly unbounded representation type. Colloquium Mathematicae, Tome 100 (2004) pp. 265-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-2-8/