An algebraic model for rational $G$-spectra over an exceptional subgroup

We give a simple algebraic model for rational $G$-spectra over an exceptional subgroup, for any compact Lie group $G$. Moreover, all our Quillen equivalences are symmetric monoidal, so as a corollary we obtain a monoidal algebraic model for rational $G$-spectra when $G$ is finite. We also present a study of the relationship between induction-restriction-coinduction adjunctions and left Bousfield localizations at idempotents of the rational Burnside ring.

Keywords

equivariant spectra, model category, algebraic model, left Bousfield localization

2010 Mathematics Subject Classification

55N91, 55P42, 55P60

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Received 23 November 2015

Received revised 22 December 2016

Published 22 November 2017