Geodesic
An algebraic model for rational naïve-commutative $G$-equivariant ring spectra for $\textrm{finite} \: G$
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 73-93.

Voir la notice de l'article provenant de la source International Press of Boston

Equipping a non-equivariant topological $E_{\infty}$-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 naïve-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 naïve-commutative ring $G$-spectra. In other words, a rational naïve-commutative ring $G$-spectrum is given in the algebraic model by specifying a $\mathbb{Q} [W_G (H)]$-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 $G$.
DOI : 10.4310/HHA.2019.v21.n1.a4
Classification : 55N91, 55P42, 55P60
Keywords: rational equivariant spectrum, commutative equivariant ring spectrum, left Bousfield localisation, model category, algebraic model 
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     author = {Barnes David and J.P.C. Greenlees and Magdalena K\c{e}dziorek},
     title = {An algebraic model for rational na{\"\i}ve-commutative $G$-equivariant ring spectra for $\textrm{finite} \: G$},
     journal = {Homology, homotopy, and applications},
     pages = {73--93},
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}
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Barnes David; J.P.C. Greenlees; Magdalena Kȩdziorek. An algebraic model for rational naïve-commutative $G$-equivariant ring spectra for $\textrm{finite} \: G$. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 73-93. doi : 10.4310/HHA.2019.v21.n1.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a4/

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