AN ALGEBRAIC MODEL FOR RATIONAL NAIVE-COMMUTATIVE G-EQUIVARIANT RING SPECTRA FOR FINITE G

Equipping a non-equivariant topological E-infinity-operad with the trivial G-action gives an operad in G-spaces. The algebra structure encoded by this operad in G-spectra is characterised homotopically by having no non-trivial multiplicative norms. Algebras over this operad are called naive-commutative ring G-spectra. In this paper we let G be a finite group and we show that commutative algebras in the algebraic model for rational G-spectra model the rational naive-commutative ring G-spectra. In other words, a rational naive-commutative ring G-spectrum is given in the algebraic model by specifying a Q[W-G(H)]-differential graded algebra for each conjugacy class of subgroups H of G. Here W-G(H) = N-G(H)/H is the Weyl group of H in G.