An Introduction to Algebraic Models for Rational G–Spectra
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Cambridge : Cambridge University Press
London Mathematical Society Lecture Note Series ; 474
InBarnes, D.; Kędziorek, M.; Szymik, M. (ed.), Equivariant Topology and Derived Algebra, pp. 119-179
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Barnes, D.; Kędziorek, M.; Szymik, M. (ed.), Equivariant Topology and Derived Algebra
SubjectLondon Mathematical Society Lecture Note Series; Mathematics
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.
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