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

TL;DR

This paper develops a simplified algebraic framework for understanding rational G-spectra over exceptional subgroups in compact Lie groups, establishing symmetric monoidal equivalences and exploring adjunctions and localizations.

Contribution

It introduces a new algebraic model for rational G-spectra over exceptional subgroups that is symmetric monoidal, extending to finite groups and analyzing key adjunctions.

Findings

Established a symmetric monoidal algebraic model for rational G-spectra over exceptional subgroups.

Extended the model to finite groups, providing a monoidal algebraic framework.

Analyzed the interplay between induction, restriction, coinduction, and localizations in the context of the rational Burnside ring.

Abstract

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.