Fusion Systems in Algebra and Topology
Fusion Systems in Algebra and Topology
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DOI：
10.1017/cbo9781139003841
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Aschbacher;R. Kessar;B. Oliver
中科院分区：
文献类型：
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作者：
M. Aschbacher;R. Kessar;B. Oliver
p-群S上的融合系统是一个范畴，其对象形成S的所有子群的集合，其态射是某些内射群同态，并且满足普伊格首先以有限群中的共轭关系为模型而制定的公理。这个定义最初是由表示论提出的，但融合系统也可以应用于局部群论和同伦理论。与同伦理论的联系是通过分类空间产生的，这些空间可以与融合系统相关联，并且具有有限群的p-完全分类空间的许多良好性质。从详细阐述的基础材料开始，作者接着讨论融合系统在局部有限群理论，同伦理论和模表示理论中的作用。这本书作为一个基本的参考和介绍该领域，特别是学生和其他年轻的数学家。
A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.