Algebraic models for 1-dimensional categories of rational G-spectra

TL;DR

This paper develops algebraic models for rational G-spectra in 1-dimensional isotropy cases, extending previous results for specific groups to a broader class of compact Lie groups with 1-dimensional isotropy blocks.

Contribution

It generalizes existing algebraic models for rational G-spectra from specific groups to a wider class of compact Lie groups with 1-dimensional isotropy.

Findings

Algebraic models constructed for rational G-spectra with 1-dimensional isotropy.

Includes all blocks of groups of dimension 1 and semifree spectra.

Extends previous results from G=SO(2) or O(2) to more general groups.

Abstract

In this paper we give algebraic models for rational G-spectra for a compact Lie group G when the geometric isotropy is restricted to lie in a 1-dimensional block of conjugacy classes. This includes all blocks of all groups of dimension 1, semifree spectra, and 1-dimensional blocks for many other groups G. The results were known previously for G=SO(2) or O(2) due to work of Barnes, Shipley and the author.