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  An algebraic model for rational naive-commutative G-equivariant ring spectra for finite G

Barnes, D., Greenlees, J. P. C., & Kędziorek, M. (2019). An algebraic model for rational naive-commutative G-equivariant ring spectra for finite G. Homology, Homotopy and Applications, 21(1), 73-93. doi:10.4310/HHA.2019.v21.n1.a4.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-8A17-7 Version Permalink: https://hdl.handle.net/21.11116/0000-000D-CAD8-C
Genre: Journal Article
Latex : An algebraic model for rational naive-commutative $G$-equivariant ring spectra for finite $G$

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 Creators:
Barnes, David, Author
Greenlees, J. P. C., Author
Kędziorek, Magdalena1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Topology
 Abstract: 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 $G$.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 21
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1708.09003
DOI: 10.4310/HHA.2019.v21.n1.a4
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Title: Homology, Homotopy and Applications
Source Genre: Journal
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Publ. Info: International Press
Pages: - Volume / Issue: 21 (1) Sequence Number: - Start / End Page: 73 - 93 Identifier: -