Freyd's Generating Hypothesis for Groups with Periodic Cohomology

Canadian mathematical bulletin

Ján Miná?²  J. Daniel Christensen²  Sunil K. Chebolu¹ 

[1] Department of Mathematics, Illinois State University, Normal, IL 61761, U.S.A.;Department of Mathematics, University of Western Ontario, London, ON N6A 5B7

关键词: Tate cohomology;    generating hypothesis;    stable module category;    ghost map;    principal block;    thick subcategory;    periodic cohomology;   

DOI  :  10.4153/CMB-2011-090-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $G$ be a finite group, and let $k$ be a field whose characteristic $p$divides the order of $G$.Freyd's generating hypothesis for the stable module category of$G$ is the statement that a map between finite-dimensional$kG$-modules in the thick subcategory generated by $k$ factors through aprojective if the induced map on Tate cohomology is trivial. We show that if$G$has periodic cohomology, then the generating hypothesis holds if and only ifthe Sylow$p$-subgroup of $G$ is $C_2$ or $C_3$. We also give some other conditionsthat are equivalent to the GHfor groups with periodic cohomology.

【 授权许可】

Unknown