An introduction to algebraic models for rational G-spectra

David Barnes, Magdalena Kedziorek

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


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 chapter 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-spectra in terms of a symmetric monoidal algebraic category. Having these two parts in the same place allows one to see clearly the analogy between the algebraic and topological classifications.

Original languageEnglish
Title of host publicationEquivariant topology and derived algebra
EditorsScott Balchin, David Barnes, Magdalena Kędziorek, Markus Szymik
PublisherCambridge University Press
ISBN (Electronic)9781108942874
ISBN (Print)9781108931946
Publication statusPublished - 29 Oct 2021

Publication series

NameLondon Mathematical Society Lecture Note Series


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