Decomposing thick subcategories of the stable module category

Krause H (1999)
Mathematische Annalen 313(1): 95-108.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
Mathematische Annalen
Band
313
Ausgabe
1
Seite(n)
95-108
ISSN
PUB-ID

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Krause H. Decomposing thick subcategories of the stable module category. Mathematische Annalen. 1999;313(1):95-108.
Krause, H. (1999). Decomposing thick subcategories of the stable module category. Mathematische Annalen, 313(1), 95-108. doi:10.1007/s002080050252
Krause, H. (1999). Decomposing thick subcategories of the stable module category. Mathematische Annalen 313, 95-108.
Krause, H., 1999. Decomposing thick subcategories of the stable module category. Mathematische Annalen, 313(1), p 95-108.
H. Krause, “Decomposing thick subcategories of the stable module category”, Mathematische Annalen, vol. 313, 1999, pp. 95-108.
Krause, H.: Decomposing thick subcategories of the stable module category. Mathematische Annalen. 313, 95-108 (1999).
Krause, Henning. “Decomposing thick subcategories of the stable module category”. Mathematische Annalen 313.1 (1999): 95-108.