The ideals of the slice Burnside p-biset functor

TL;DR

This paper investigates the structure of ideals within the slice Burnside p-biset functor over a field of characteristic zero, providing a detailed description of their lattice and properties.

Contribution

It characterizes the ideals of the slice Burnside functor K{ extbackslash Xi}p, showing they correspond to subfunctors with ideal evaluations at each finite group.

Findings

Identifies the subfunctors that form the ideals of K{ extbackslash Xi}p

Determines the full lattice of ideals for the functor

Provides criteria for subfunctors to be ideals

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.