The generating hypothesis for the stable module category of a p-group

JOURNAL OF ALGEBRA

卷:310

Article

Benson, David J. ; Chebolu, Sunil K. ; Christensen, J. Daniel ; Minac, Jan

关键词: generating hypothesis;    stable module category;    ghost map;   

DOI  :  10.1016/j.jalgebra.2006.12.013

来源: Elsevier

【 摘 要 】

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the induced map on Tate cohomology is trivial. We show that Freyd's generating hypothesis holds for a non-trivial finite p-group G if and only if G is either C-2 or C-3. We also give various conditions which are equivalent to the generating hypothesis. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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