Naive-commutative structure on rational equivariant K-theory for abelian groups

Abstract

In this paper, we calculate the image of the connective and periodic rational equivariant complex K-theory spectrum in the algebraic model for naive-commutative ring G-spectra given by Barnes, Greenlees and Kędziorek for finite abelian G. Our calculations show that these spectra are unique as naive-commutative ring spectra in the sense that they are determined up to weak equivalence by their homotopy groups. We further deduce a structure theorem for module spectra over rational equivariant complex K-theory.