An algebraic model for free rational \(G\)-spectra for connected compact Lie groups \(G\) (Q641888)

Let \(G\) be a connected compact Lie group, and let \(H^*(BG)\) be the rational cohomology ring of its classifying space \(BG\). The authors show that the category of free rational \(G\)-spectra is Quillen equivalent to the category of torsion differential graded \(H^*(BG)\)-algebras. Given a connected compact subgroup \(H\) of \(G\), they also show that various functors between \(G\)-spectra and \(H\)-spectra correspond to the appropriate functors between \(H^*(BG)\)-modules and \(H^*(BH)\)-modules.