The $A$-fibered Burnside ring as $A$-fibered biset functor in characteristic zero.

@article{Boltje2019TheB,
title={The \$A\$-fibered Burnside ring as \$A\$-fibered biset functor in characteristic zero.},
author={Robert Boltje and D. Yılmaz},
journal={arXiv: Representation Theory},
year={2019}
}

Let $A$ be an abelian group and let $\mathbb{K}$ be a field of characteristic zero containing roots of unity of all orders equal to finite element orders in $A$. In this paper we prove foundational properties of the $A$-fibered Burnside ring functor $B_{\mathbb{K}}^A$ as an $A$-fibered biset functor over $\mathbb{K}$. This includes the determination of the lattice of subfunctors of $B_{\mathbb{K}}^A$ and the determination of the composition factors of $B_{\mathbb{K}}^A$. The results of the… CONTINUE READING