Finite localities I
Finite localities I
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有限地点 I
DOI：
10.1017/fms.2022.31
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Chermak
中科院分区：
文献类型：
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作者：
A. Chermak
这是关于“局部分组空间”的一系列论文中的第一篇，与代数几何中的局部环空间有一个松散的类比。我们心目中的空间是单纯集，它推广了构成和决定有限(或紧)群的分类空间的单纯集。如果进行类比，那么“结构束”的作用是由与这些空间相关联的“融合系统”提供的。我们在这里的方法将是纯粹的代数和组合，所以我们不关心拓扑实现。所有要审议的小组都将是有限的；但代表与亚历克斯·冈萨雷斯共同工作的一系列平行文件将极大地扩大范围。
This is the first of a series of papers concerning what might be thought of as ‘locally grouped spaces’, in a loose analogy with the locally ringed spaces of algebraic geometry. The spaces that we have in mind are simplicial sets that generalise the simplicial sets that underlie and determine the classifying spaces of finite (or compact) groups. If the analogy is pursued, then the role of ‘structure sheaf’ is provided by the ‘fusion systems’ associated with these spaces. Our approach here will be purely algebraic and combinatorial, so we will not be concerned with topological realisations. All of the groups to be considered will be finite; but a parallel series of papers representing some joint work with Alex Gonzalez will considerably broaden the scope.