The slice Burnside ring and the section Burnside ring of a finite group
The slice Burnside ring and the section Burnside ring of a finite group
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有限群的切片Burnside环和截面Burnside环
DOI：
10.1112/s0010437x11007500
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发表时间：
2011
影响因子：
1.8
通讯作者：
S. Bouc
中科院分区：
文献类型：
--
作者：
S. Bouc
本文在有限群G上引入了两个新的伯恩赛德环，称为切片伯恩赛德环和截伯恩赛德环.它们分别被构造为G-集的态射范畴和G-集的Galois态射范畴的Grothendieck环。著名的结果通常伯恩赛德环，鬼地图，本原幂等元，并描述了素谱，推广到这些环。证明了这两个环具有自然的绿色偏集函子结构。还讨论了这些环的单位群的函子结构。
Abstract This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets and of Galois morphisms of G-sets, respectively. The well-known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are extended to these rings. It is also shown that these two rings have a natural Green biset functor structure. The functorial structure of unit groups of these rings is also discussed.