Classifying Dihedral O(2)-Equivariant Spectra

TL;DR

This paper provides an algebraic classification of the dihedral component of rational O(2)-equivariant spectra, enhancing understanding of their structure by leveraging the classification of spectra for finite groups.

Contribution

It introduces a novel algebraic model specifically for the dihedral part of rational O(2)-spectra, building on existing classifications for finite groups.

Findings

The dihedral part of rational O(2)-spectra is classified algebraically.

The category of rational O(2)-spectra splits into cyclic and dihedral components.

An explicit algebraic model for the dihedral spectra is constructed.

Abstract

The category of rational O(2)-equivariant spectra splits as a product of cyclic and dihedral parts. Using the classification of rational G-equivariant spectra for finite groups G, we classify the dihedral part of rational O(2)-equivariant spectra in terms of an algebraic model.