Algebras over equivariant sphere spectra Original Research Article

We study the category of algebras over the sphere G-spectrum of a compact Lie group G. A priori, this category depends on which representations appear in the underlying universe on which G-spectra are indexed, but we prove that different universes give rise to equivalent categories of point-set level algebras. The relevant change of universe functors are defined on categories of modules over sphere spectra and induce the classical change of universe functors (which are not equivalences!) on passage to stable homotopy categories. In particular, we show how to construct equivariant algebras from nonequivariant algebras by change of universe. This gives a reservoir of equivariant examples to which recently developed algebraic techniques in stable homotopy theory can be applied.