On twisted group algebras of OTP representation type

Tom 127 / 2012

Leonid F. Barannyk, Dariusz Klein Colloquium Mathematicum 127 (2012), 213-232 MSC: Primary 16G60; Secondary 20C20, 20C25. DOI: 10.4064/cm127-2-5

Streszczenie

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 $S^\lambda G$ the twisted group algebra of $G$ over $S$ with a $2$-cocycle $\lambda \in Z^2(G,S^*)$. We give necessary and sufficient conditions for $S^\lambda G$ to be of OTP representation type, in the sense that every indecomposable $S^\lambda G$-module is isomorphic to the outer tensor product $V\mathbin {\#}W$ of an indecomposable $S^\lambda G_p$-module $V$ and an irreducible $S^\lambda B$-module $W$.

Autorzy

  • Leonid F. BarannykInstitute of Mathematics
    Pomeranian University of Słupsk
    Arciszewskiego 22d
    76-200 Słupsk, Poland
    e-mail
  • Dariusz KleinInstitute of Mathematics
    Pomeranian University of Słupsk
    Arciszewskiego 22d
    76-200 Słupsk, Poland
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek