PUB - Publikationen an der Universität Bielefeld

Let <(mod)under bar> kG be the stable category of finitely generated modular representations of a finite group G over a held Ic. We prove a Krull-Remak-Schmidt theorem for thick subcategories of <(mod)under bar> kG. It is shown that every thick tenser-ideal C of <(mod)under bar> kG (i.e. a thick subcategory which is a tensor ideal) has a (usually infinite) unique decomposition C = coproduct C-i is an element of I(i) into indecomposable thick tenser-ideals. This decomposition follows from a decomposition of the corresponding idempotent kG-module E-C into indecomposable modules. If C = C-W is the thick tenser-ideal corresponding to a closed homogeneous subvariety W of the maximal ideal spectrum of the cohomology ring H*(G, k), then the decomposition of C reflects the decomposition W = boolean ORi=1n W-i of W into connected components.