Generic Idempotent Modules for a Finite Group |
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Authors: | D J Benson H Krause |
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Institution: | (1) Department of Mathematics, University of Georgia, Athens, GA, 30602, U.S.A.;(2) Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany. e-mail |
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Abstract: | Let G be a finite group and k an algebraically closed field of characteristic p. Let F
U
be the Rickard idempotent k G-module corresponding to the set U of subvarieties of the cohomology variety V
G
which are not irreducible components. We show that F
U
is a finite sum of generic modules corresponding to the irreducible components of V
G
. In this context, a generic module is an indecomposable module of infinite length over k G but finite length as a module over its endomorphism ring. |
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Keywords: | finite group modular representation theory idempotent module generic module cohomology variety |
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