论文标题
理性G-Spectra代数模型简介
An introduction to algebraic models for rational G-spectra
论文作者
论文摘要
Greenlees等人的项目。在理解有限的G-Spectra方面，在代数类别方面取得了许多成功，对有限组的理性G-Spectra进行了分类，因此（2），O（2），SO（3），自由和无cofre and cofree and cofe and cofe g-spectra以及合理的toral g-spectra以及任意紧凑型组的理性G-Spectra。 本文为主题提供了两个部分的介绍。第一个讨论了理性的G-Mackey函数，Burnside环的作用以及组函子的变化。它提供了有限G的理性Mackey函子的众所周知分类的完整证明。第二部分讨论了获得等效稳定同型理论的方法和工具，以获取用于理性G-Spectra的代数模型所需的代数模型。它总结了对称单体代数类别的理性G-spectrain术语分类的关键步骤。 将这两个部分放在同一地点可以清楚地看到代数和拓扑分类之间的类比。
The project of Greenlees et al. on understanding rational G-spectra in terms of algebraic categories has had many successes, classifying rational G-spectra for finite groups, SO(2), O(2), SO(3), free and cofree G-spectra as well as rational toral G-spectra for arbitrary compact Lie groups. This paper provides an introduction to the subject in two parts. The first discusses rational G-Mackey functors, the action of the Burnside ring and change of group functors. It gives a complete proof of the well-known classification of rational Mackey functors for finite G. The second part discusses the methods and tools from equivariant stable homotopy theory needed to obtain algebraic models for rational G-spectra. It gives a summary of the key steps in the classification of rational G-spectrain terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to clearly see the analogy between the algebraic and topological classifications.
