On twisted group algebras of OTP representation type

Leonid F. Barannyk; Dariusz Klein

Colloquium Mathematicae, Tome 126 (2012), p. 213-232 / Harvested from The Polish Digital Mathematics Library

Résumé

Assume that S is a commutative complete discrete valuation domain of characteristic p, S* is the unit group of S and $G = G_{p} \times B$ is a finite group, where $G_{p}$ is a p-group and B is a p’-group. Denote by $S^{λ} G$ the twisted group algebra of G over S with a 2-cocycle λ ∈ Z²(G,S*). We give necessary and sufficient conditions for $S^{λ} G$ to be of OTP representation type, in the sense that every indecomposable $S^{λ} G$ -module is isomorphic to the outer tensor product V W of an indecomposable $S^{λ} G_{p}$ -module V and an irreducible $S^{λ} B$ -module W.

Publié le : 2012-01-01

Zbl 1263.16027

EUDML-ID : urn:eudml:doc:284264

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     title = {On twisted group algebras of OTP representation type},
     journal = {Colloquium Mathematicae},
     volume = {126},
     year = {2012},
     pages = {213-232},
     zbl = {1263.16027},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm127-2-5}
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Leonid F. Barannyk; Dariusz Klein. On twisted group algebras of OTP representation type. Colloquium Mathematicae, Tome 126 (2012) pp. 213-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm127-2-5/