Idempotent Modules in the Stable Category
Idempotent Modules in the Stable Category
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稳定类别中的幂等模块
DOI：
10.1112/s0024610797005309
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Rickard
中科院分区：
文献类型：
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作者：
J. Rickard
设G是有限群，k是具有素特征的代数闭域。对应于H*(G，k)的极大理想谱的每个闭齐次子簇W，我们构造了(通常是无穷维的)Kg模E(W)和F(W)，它们在某种意义上是幂等的，即E(W)和F(W)分别与E(W)、⊗E(W)和F(W)⊗F(W)同构。我们研究了这些模的性质，作为应用，我们用它们来刻画商范畴中模的自然直和分解。
Let G be a finite group and k be an algebraically closed field of prime characteristic. Corresponding to each closed homogeneous subvariety W of the maximal ideal spectrum of H*(G, k) we construct (usually infinite‐dimensional) kG‐modules E(W) and F(W) which are idempotent in the sense that E(W) and F(W) are isomorphic (up to projective summands) to E(W) ⊗ E(W) and F(W) ⊗ F(W) respectively. We study the properties of these modules, and as an application we use them to describe natural direct sum decompositions of modules in quotient categories.