Saturated fusion systems as idempotents in the double Burnside ring
Saturated fusion systems as idempotents in the double Burnside ring
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双 Burnside 环中幂等的饱和融合系统
DOI：
10.2140/gt.2013.17.839
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发表时间：
2009
影响因子：
2
通讯作者：
R. Stancu
中科院分区：
文献类型：
--
作者：
Kári Ragnarsson;R. Stancu
利用S的p-局部双伯恩赛德环中满足Frobenius互易关系的幂等元，给出了p-群S上饱和融合系统的一个新刻画.在稳定同伦中解释我们的结果，我们刻画了具有饱和融合系统分类谱同伦类型的有限p-群的分类空间的稳定和项，并证明了一个二重伯恩赛德模的不变定理，类似于初等交换p-群的上同调不变量环的亚当斯-威尔克森准则.这项工作的部分动机是海恩斯米勒的一个猜想，提出p-域群作为p-局部有限群的纯同伦理论模型。我们证明了当两个技术假设成立时，p-tract群会产生p-local有限群，从而将猜想简化为证明这两个假设。20D20、55R35; 55P42、19A22
We give a new characterization of saturated fusion systems on a p ‐group S in terms of idempotents in the p ‐local double Burnside ring of S that satisfy a Frobenius reciprocity relation. Interpreting our results in stable homotopy, we characterize the stable summands of the classifying space of a finite p ‐group that have the homotopy type of the classifying spectrum of a saturated fusion system, and prove an invariant theorem for double Burnside modules analogous to the Adams‐Wilkerson criterion for rings of invariants in the cohomology of an elementary abelian p ‐group. This work is partly motivated by a conjecture of Haynes Miller that proposes p ‐tract groups as a purely homotopy-theoretical model for p ‐local finite groups. We show that a p ‐tract group gives rise to a p ‐local finite group when two technical assumptions are made, thus reducing the conjecture to proving those two assumptions. 20D20, 55R35; 55P42, 19A22
西格尔猜想和聚变系统的伯恩赛德环
DOI：
10.1112/jlms/jdp048
发表时间：
2009
期刊：
Journal of the London Mathematical Society
影响因子：
--
作者：
Díaz A
通讯作者：
Díaz A