The ideals of the slice Burnside p-biset functor

Abstract

Let G be a finite group and K be a field of characteristic zero. Our purpose is to investigate the ideals of the slice Burnside functor K{\Xi}. It turns out that they are the subfunctors F of K{\Xi} such that for any finite group G, the evaluation F(G) is an ideal of the algebra K{\Xi}(G). This allows for a determination of the full lattice of ideals of the slice Burnside p-biset functor K{\Xi}p.