An algebraic model for rational $\mathrm{SO}(3)$–spectra

Abstract

Greenlees established an equivalence of categories between the homotopy category of rational $SO\left(3\right)$–spectra and the derived category $d\mathcal{A}\left(SO\left(3\right)\right)$ of a certain abelian category. In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. Methods used in this paper provide the first step towards obtaining an algebraic model for the toral part of rational $G$–spectra, for any compact Lie group $G$.